We present the results of a 42-orbit Hubble Space Telescope Wide-Field Camera 3 (HST/WFC3) survey of the rest-frame optical morphologies of star-forming galaxies with spectroscopic redshifts in the range z = 1.5-3.6. The survey consists of 42 orbits of F160W imaging covering ~65 arcmin2 distributed widely across the sky and reaching a depth of 27.9 AB for a 5σ detection within a 0.2 arcsec radius aperture. Focusing on an optically selected sample of 306 star-forming galaxies with stellar masses in the range M_* = 10^9-10^(11) M_☉, we find that typical circularized effective half-light radii range from ~0.7 to 3.0 kpc and describe a stellar mass-radius relation as early as z ~ 3. While these galaxies are best described by an exponential surface brightness profile (Sérsic index n ~ 1), their distribution of axis ratios is strongly inconsistent with a population of inclined exponential disks and is better reproduced by triaxial stellar systems with minor/major and intermediate/major axis ratios ~0.3 and 0.7, respectively. While rest-UV and rest-optical morphologies are generally similar for a subset of galaxies with HST/Advanced Camera for Surveys imaging data, differences are more pronounced at higher masses M_* > 3 × 10^(10) M_☉. Finally, we discuss galaxy morphology in the context of efforts to constrain the merger fraction, finding that morphologically identified mergers/non-mergers generally have insignificant differences in terms of physical observables such as stellar mass and star formation rate, although merger-like galaxies selected according to some criteria have statistically smaller effective radii and correspondingly larger Σ_(SFR).