"To tire" is to make someone else tired. If someone is tired (in a state of being tired) themselves, you use the auxiliary verb "to be". The full sentence becomes "I am tired", where " tired" is an adjective.
'To tire' can be used with or without an object. Technically, 'I have tired' is correct (i.e. I have become fatigued). But people much more commonly use the adjective: I have become tired.