The Altiplano-Puna volcanic complex (APVC) is located in the central Andes and covers an area over 50,000 km2. The style of volcanism is predominately caldera-forming ignimbrite eruptions active between 10 and 1 Ma. Chmielowski et al. <1999> used teleseismic events, recorded from seven portable broadband seismic stations deployed in the APVC, to identify a 1-km-thick very low-velocity zone at a depth of 19 km. Based on the correlation with surface volcanics, the extremely low shear velocities of 1 km/s or less, and the depth of the layer, the low-velocity zone was interpreted to be a magma body. Using local events recorded during the same seismic deployment, we have improved the crustal model for the APVC and detected seismic anisotropy in the crust above the low-velocity zone. Using a hexagonal symmetry anisotropy code, we computed synthetic receiver functions for many models of layered anisotropic media and found two different models consistent with the data. In both models, approximately 20--30% anisotropy is present in a 3-km-thick surface low-velocity layer, and 15--20% anisotropy is present in the remaining crust above the buried low-velocity zone. The first model has the 1-km-thick low-velocity zone at 17 km, while the alternate model has the low-velocity zone at 14-km depth overlain by a 4-km-thick transition zone of intermediate velocities. This anisotropy may be due to the fracture system by which magma migrates to the surface from the midcrustal sill-like magma body.