Complementary metal-oxide-semiconductor (CMOS) technology has provided a highly sensitive detection platform for high-resolution optical imaging, sensing and metrology. Although the detection of optical beams carrying angular momentum have been explored with nanophotonic methods, the metrology of optical angular momentum has been limited to bulk optics. We demonstrate angular-momentum nanometrology through the spatial displacement engineering of plasmonic angular momentum modes in a CMOS-compatible plasmonic topological insulator material. The generation and propagation of surface plasmon polaritons on the surface of an ultrathin topological insulator Sb2Te3 film with a thickness of 100 nm is confirmed, exhibiting plasmonic figures of merit superior to noble metal plasmonics in the ultraviolet-visible frequency range. Angular-momentum nanometrology with a low crosstalk of less than -20 dB is achieved. This compact high-precision angular-momentum nanometrology opens an unprecedented opportunity for on-chip manipulation of optical angular momentum for high-capacity information processing, ultrasensitive molecular sensing, and ultracompact multi-functional optoelectronic devices.