Are you able to appeal a misdmeanor bench warrant after 7 years?

A warrant is merely a court order to make you appear in court. You will be charged with some crime that the warrant is for.

Since the warrant is only to bring you to the court, when you appear, to appeal what ever crime the warrant is for, you are before the court.

So you can hire an attorney to arrange for you to turn yourself in, or to appear in court to take care of the warrant, if they will allow it.