Orthogonal Shimura varieties arise from symmetric domains attached to orthogonal groups. We show that the Picard group of the Baily-Borel compactification of an orthogonal Shimura variety is isomorphic to Z if the corresponding lattice splits two hyperbolic planes globally and three hyperbolic planes locally. In particular, this is the case for the Baily-Borel compactification of the moduli space of quasi-polarized K3 surfaces. One of the main ingredients of the proof is a result on the basis problem for modular forms for the Weil representation, which states that a certain space of cusp forms is generated by theta series.