A Sorcerer's Treason (Isavalta Trilogy) by Sarah Zettel

Ostracised lighthouse keeper Bridget Lederie finds a man washed up on the shore, almost dead. When he speaks, it is in an unknown language but when he wraps a piece of braided cloth around her arm, she is able to understand him. She finds he is a wizard and he wants her to come with him to another world.