In this article, we propose a reinforcement learning (RL)-based methodology to analyze vulnerability of real-time (RT) electricity market under grid topology attack. In RT electricity market, the electricity prices at different buses in the grid network are decided based on the locational marginal price (LMP). LMP is derived from the solution to DC optimal power flow (DCOPF) which depends on the grid topology, generation cost, and real-time demand. Hence, an attacker can manipulate the topology information to alter the solution to DCOPF leading to alteration of LMPs, thus harnessing monetary profit. Our analysis entails realistic cyber-topology attack, that is, the attacker can only manipulate the breaker status, but not the physical topology, and it has no knowledge of the topology prior to attack. Under such cyber-topology attack, our proposed RL-based methodology identifies the critical breakers in the power network that, if attacked, can lead to large deviation in LMP from the actual value and disrupt the electricity market. We instantiate our proposed technique in IEEE-39 and 300 bus network and establish that the critical branches, identified by our algorithm, are crucial in terms of maintaining the stability of RT market, hence must be protected by the grid operator.