If you tried to apply to a diocesan seminary, you would have a hard time, for the reasons that others have outlined.
If you were to apply to a religious order near you, you might have a better chance. In this context, you might be able for them to get to know you personally. There may be a chance to be interviewed several times, to go for retreats, etc., and get the community to know you.* Then* when they start to discuss religious life with you, you could say that you are very interested, but have this impediment. In this way, they will see that you are “well controlled”, and not have to reply on your statement about it. You will certainly be under close observation during the formative years, but everyone is. You will also have to have the opportunity to see your psychiatrist and other mental health care providers on a regular basis.