It depends on what you not having "patience" in chess means.
If you imply that black plays passively because white moves first, then this isn't 100% correct. GM Bobby Fischer said that one of the pivotal moments for his chess was the moment he realized that black can be playing for a win.
If instead you mean that you move too impulsively, then playing another another color won't help with this, but perhaps the old method of literally "sitting on your hands" will help. It gives you just that half a second or so longer to help you catch errors before you make them and to remind you to do a blunder check before you move. If you do this enough, that might help develop patience in chess.
Play as Black
Play as Black
Play as Black