The answer is tienes sueño.
In English, "anoche dormiste sólo una hora" means "last night you only slept for one hour." We know that the subject of the sentence is "you" due to the conjugation of the verb "dormir" (remember that subject pronouns aren't necessary in Spanish). So, the verb "tenir" must also correspond to "you" (tu tienes). Since "you" slept for only hour, we can infer that the subject is tired. In Spanish, you can say "estas cansado/a" or "tienes sueño" to say "You are tired."
