Can you become a psychiatrist if you also have a slight mental disorder?

Yes. : If you have the drive, the required resources (emotional & financial) and the physical health to sustain the effort, you can be whatever you want. Good luck!

Depends on disorder: Being a psychiatrist requires you to put your issues aside as much as possible when attending to your patient's needs. Most humans are anxious or conflicted about something. Depending on degree, this does not interfere with ability to work -- even in a stressful profession requiring focus and empathy like psychiatry. Many psychiatrists also get personal help as needed -- and you can too.