You can mention in your PS that you are a re-applicant, but it's not by any means necessary. Personally, in my PS, I did mention that I am a re-applicant during the process of explaining what I've been doing to explore medicine/reaffirm that this is the right career path for me. Needless to say, I didn't make my re-applicant status the focus of my essay.
Truly there really is not a huge need to bring this fact out. You will face this question again with your secondaries ... so if you need space in your PS, just wait till your secondaries to talk about your previous rejection and what you learned/what you did to strengthen your application.