Moire superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moire heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moire excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moire physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TMDC. Here we report emerging anisotropic moire optical transitions in twisted monolayer/bilayer phosphorene. The optical resonances in phosphorene moire superlattice depend sensitively on the twist angle between the monolayer and bilayer. Surprisingly, even for a twist angle as large as 19{deg} the moire heterostructure exhibits optical resonances completely different from those in the constituent monolayer and bilayer phosphorene. The new moire optical resonances exhibit strong linear polarization, with the principal axis lying close to but different from the optical axis of bilayer phosphorene. Our ab initio calculations reveal that the {Gamma}-point direct bandgap and the rectangular lattice of phosphorene, unlike the K-point bandgap of hexagonal lattice in graphene and TMDC, give rise to the remarkably strong moire physics in large-twist-angle phosphorene heterostructures. Our results highlight the exciting opportunities to explore moire physics in phosphorene and other van der Waals heterostructures with different lattice configurations.