An on-chip high-frequency testing method for rapid single flux quantum circuits is proposed. This method employs test vectors based on pseudo-random sequences created by an on-chip high-frequency clock generator (CG) and a linear feedback shift register with parallel outputs (LSPO). Downsamplers (DSMs) at the outputs of a circuit under test (CUT) decimate the CUT output data so that high-frequency testing can be performed at sufficiently low data rates between the CUT and room-temperature electronics. The proposed testing can continuously test the circuit at high frequency with low-cost instruments. All of the critical subsystems, including LSPO, CG, and DSM, were designed, fabricated, and successfully tested. We validated proper operation at up to 40 GHz, confirming the concept and execution.