Using Hubble Space Telescope/WFC3 imaging taken as part of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, we examine the role that major galaxy mergers play in triggering active galactic nucleus (AGN) activity at z similar to 2. Our sample consists of 72 moderate-luminosity (L-X similar to 10(42-44) erg s(-1)) AGNs at 1.5 < z < 2.5 that are selected using the 4 Ms Chandra observations in the Chandra Deep Field South, the deepest X-ray observations to date. Employing visual classifications, we have analyzed the rest-frame optical morphologies of the AGN host galaxies and compared them to a mass-matched control sample of 216 non-active galaxies at the same redshift. We find that most of the AGNs reside in disk galaxies (51.4(-5.9)(+5.8)%), while a smaller percentage are found in spheroids (27.8(-4.6)(+5.8)%). Roughly 16.7(-3.5)(+5.3)% of the AGN hosts have highly disturbed morphologies and appear to be involved in a major merger or interaction, while most of the hosts (55.6(-5.9)(+5.6)%) appear relatively relaxed and undisturbed. These fractions are statistically consistent with the fraction of control galaxies that show similar morphological disturbances. These results suggest that the hosts of moderate-luminosity AGNs are no more likely to be involved in an ongoing merger or interaction relative to non-active galaxies of similar mass at z similar to 2. The high disk fraction observed among the AGN hosts also appears to be at odds with predictions that merger-driven accretion should be the dominant AGN fueling mode at z similar to 2, even at moderate X-ray luminosities. Although we cannot rule out that minor mergers are responsible for triggering these systems, the presence of a large population of relatively undisturbed disk-like hosts suggests that the stochastic accretion of gas plays a greater role in fueling AGN activity at z similar to 2 than previously thought.