Planet-planet scattering has long been a contender for the dynamical process that produces the eccentricities of observed close-in giant planets. In the inner regions of planetary systems, however, planet-planet scattering inevitably leads to giant impacts. In this work, we consider whether a giant impacts phase for gas giants could have produced the observed population of eccentric giants discovered using the Radial Velocity method. Many of these objects are substantially more massive than Jupiter, rendering plausible the idea that the formed initially as smaller gas giants, which coalesced to form behemoths. We conduct a series of simulations using planetary systems with a distribution of initial total mass in planets. The initial conditions are otherwise quite generic. We show that a giant impacts phase can reproduce the observed upper bound on the distribution of giant planet eccentricities with semi-major axis. Importantly, our results naturally reproduce the perhaps counterintuitive observational fact that observed eccentricities are higher for higher-mass gas giants. We propose that systems that form with a larger total mass in gas giants in their inner regions typically experience a giant impacts phase that produces larger mass planets, which in turn excite each other to higher eccentricities. Critical to these results, our simulations adjust the radii of planets as they coalesce and grow, appropriately tracking their escape velocities and hence their abilities to excite the eccentricities of neighbors. We demonstrate that the eccentricity distribution of observed giant planets with semi-major axis differs for stars with high and low metallicities, in agreement with our results. We predict that mergers produce a population of high-mass giant planets between 1 and 8 AU from their host stars, consistent with tentative results from direct imaging surveys.