'Weird' can mean a lot of things.
As you can imagine, it is somewhat problematic for someone to be an effective psychiatrist if they are unable to communicate, lack empathy, dislike talking with others, etc.
If you just mean 'introverted', that shouldn't be problematic if that person can communicate appropriately/effectively with requisite people during necessary times.
All that said, residencies also want people that will be enjoyable to be around for 4-5 years...so often that is friendly/outgoing rather than cold/hermitaceous [sic].