We present a method for dependency grammar induction that utilizes sparse annotations of semantic relations. This induction set-up is attractive because such annotations provide useful clues about the underlying syntactic structure, and they are readily available in many domains (e.g., info-boxes and HTML markup). Our method is based on the intuition that syntactic realizations of the same semantic predicate exhibit some degree of consistency. We incorporate this intuition in a directed graphical model that tightly links the syntactic and semantic structures. This design enables us to exploit syntactic regularities while still allowing for variations. Another strength of the model lies in its ability to capture non-local dependency relations. Our results demonstrate that even a small amount of semantic annotations greatly improves the accuracy of learned dependencies when tested on both in-domain and out-of-domain texts.