The right answer is roto
In this sentence, the direct object pronoun me is being used. A direct object pronoun (un pronombre de objeto directo) replaces a direct object, that is a noun that directly receives the action of a verb in a sentence. me is the direct object pronoun for the first-person singular.
On the other hand, roto is an adjective and means broken. Therefore:
Yo tenía un teléfono roto cuando mi madre me llamó, translates:
I had a broken phone when my mother called me up