This is for State of Texas might be similar in other states. You can always call the licensing board helpline and they can give you career direction advise. If you want to go into R&D or work for the government in most cases you don't need a license.
Information for Persons with Criminal Backgrounds Requesting a Preliminary Evaluation of Licensure Eligibility. Board rule 469.7 allows the Texas State Board of Examiners of Psychologists to provide a preliminary evaluation of a person’s criminal background to determine if the background would prevent them from obtaining licensure with this Board. The person is required to complete an evaluation application, submit a fee and supporting documentation, and obtain a fingerprint criminal history record check in order for the Board to conduct this evaluation. An application packet for a criminal history evaluation of licensure eligibility is available at no cost by submitting a written request to the Enforcement Division of the Texas State Board of Examiners of Psychologists. Board rule 469.7 Persons with Criminal Backgrounds. (a) The Board may revoke or suspend an existing valid license, disqualify a person from receiving or renewing a license, or deny to a person the opportunity to be examined for a license due to a felony or misdemeanor conviction if the offense directly relates to the performance of the activities of a licensee and the conviction directly affects such person's present fitness to perform as a licensee of this Board. (b) Criminal History Evaluation Letters: (1) In compliance with Chapter 53 of the Texas Occupations Code, the Board will provide criminal history evaluation letters. (2) A person may request the Board to provide a criminal history evaluation letter if the person is planning to enroll or is enrolled in an educational program that prepares the person for a license with this Board and the person has reason to believe that the person is ineligible for licensure due to a conviction or deferred adjudication for a felony or misdemeanor offense. (3) The requestor must submit to the Board a completed Board application form requesting an evaluation letter, the required fee, and certified copies of court documentation about all convictions and resolution to the Board. (4) Before submitting the application the requestor must obtain a fingerprint criminal history record check and have it mailed directly to the Board. (5) The Board has the authority to investigate a request for a criminal history evaluation letter and may require that the requestor provide additional information about the convictions and other dispositions if requested by the Board. (6) The Board will provide a written response to the requestor within 90 days of the Board’s receipt of the request, unless a more extensive investigation is required or the requestor fails to comply with a Board investigation. The Board’s evaluation letter will state the Board’s determination on each ground for potential ineligibility presented by the requestor. (7) In the absence of new evidence known to but not disclosed by the requestor or not reasonably available to the Board at the time the letter is issued, the Board’s ruling on the request determines the requestor’s eligibility only with respect to the grounds for potential ineligibility set out in the letter. (c) The Board shall revoke an existing valid license, disqualify a person from receiving or renewing a license, or deny to a person the opportunity to be examined for a license due to a felony conviction under Section 35A.02 of the Texas Penal Code, concerning Medicaid fraud. (d) No person currently serving a sentence in prison for a felony is eligible to obtain or renew his/her license. (e) In determining whether a criminal conviction directly relates to the performance of a licensee, the Board shall consider the factors listed in the Texas Occupations Code, Chapter 53. (f) Those crimes which the Board considers as directly related to the performance of a licensee include but are not limited to: (1) a misdemeanor and/or felony offense under the following titles of the Texas Penal Code: (A) Title 5, pertaining to offenses against the person (for example, homicide, kidnapping, sexual offenses, and assaultive offenses); (B) Title 7, pertaining to offenses against property (for example, arson, robbery, burglary, theft, fraud, money laundering, and insurance fraud); (C) Title 8, pertaining to offenses against public administration (for example, bribery, perjury, and obstruction of justice); (D) Title 9, pertaining to offenses against public order and decency (for example, disorderly conduct and public indecency); (E) Title 10, pertaining to offenses against public health and safety (for example, weapons offenses, gambling, and intoxication offenses); and (F) Title 4, pertaining to the offenses of attempting or conspiring to commit the offenses listed in subsections (a) - (e) of this section. (2) any criminal violation of the Psychologists' Licensing Act or other statutes regulating or pertaining to the profession of psychology; (3) any criminal violation of statutes regulating other professions in the healing arts, which includes, but is not limited to medicine and nursing; (4) any crime involving moral turpitude; (5) any offense involving the failure to report abuse; (6) any state or federal drug offense, including violations of the Controlled Substances and Dangerous Drugs Act; and (7) any other misdemeanor or felony that the Board may consider in order to promote the public safety and welfare, as well as the intent of the Act and these rules. (g) In determining whether a criminal conviction directly affects present fitness of the licensee, the Board shall consider the factors listed in Texas Occupations Code, Section 53.023. (h) It shall be the responsibility of the licensee to secure and provide to the Board the recommendations of the prosecution, law enforcement, and correctional authorities regarding all criminal offenses. (i) The licensee shall also furnish proof in such form as may be required by the Board that he/she maintained a record of steady employment and has supported his/her dependents and has otherwise maintained a record of good conduct and has paid all outstanding court costs, supervision fees, fines and restitution as may have been ordered in all criminal cases in which he/she has been convicted.