This letter develops a novel transmit beamforming (BF) design for canceling self-interference (SI) in analog in-band full-duplex phased arrays. Our design maximizes transmit BF gain in a desired direction while simultaneously reducing SI power to below a specified threshold on per-antenna basis to avoid saturating receive-chain components, such as LNAs. Core to our approach is that it accounts for real-world phase shifters used in analog phased array systems, whose limited resolution imposes non-convex constraints on BF design. We overcome this by transforming these non-convex constraints into convex polygon constraints, which we then solve through semidefinite relaxation and a rank refinement procedure. Numerical results show that our proposed BF scheme reliably cancels SI to the target power threshold at each receive antenna while sacrificing little in transmit BF gain, even with modest phase shifter resolution.