Has your bird already been exposed? Would it be something you are using on yourself personally, in another room in your home or on the birds themselves? It is a good rule to never use essential oils on a bird and try to avoid using them in a closed space. Essential oils are highly concentrated from the plant (so not the same as if the bird ate the plant), usually extracted with some kind of alcohol (very bad for birds) and sometimes blended with other things that are not on the label (especially if used for scent and not made to be eaten by people which is usually shown by the words "not for human consumption"). All of that gets into the air and our lungs as it diffuses.
A better option would be to buy some dried mint leaves or mint tea and put it in a bowl to let the natural scent diffuse.