What does it mean if you have the portrait of the woman on your T-shirt and a phrase etre mon amour on it?

"être" is the infinitive for "to be"; "mon amour" means "my Love". If the message was "be my Love / be my loved one / be mine", the French expression would be "sois (imperative mood for 'to be') mon amour / sois mienne".

Hence the message certainly revolves about the same theme, even though it does not seems idiomatic in French.