This is a Phase 2, multicenter, randomized, double-blind, placebo-controlled, parallel group study to evaluate the efficacy and safety of two doses of VTX958 tablets, Dose A and Dose B, in adults with active Psoriatic Arthritis. Approximately 195 participants will be assigned in a 1:1:1 ratio to one of three groups, VTX958 Dose A, VTX958 Dose B, or placebo, for 16 weeks and then move on to a 36 week Long Term Extension (LTE). The study consists of a 30-day screening period, a 16 week double-blind treatment period, 36 weeks of LTE, and a 30 day follow-up period.