We present ~0.5" resolution near-infrared integral field spectroscopy of the Halpha line emission of 14 z~2 UV-selected BM/BX galaxies, obtained with SINFONI at the ESO Very Large Telescope. The average Halpha half-light radius is r1/2~4 h-170 kpc, and line emission is detected over >~20 h-170 kpc in several sources. In nine galaxies, we detect spatially resolved velocity gradients, from 40 to 410 km s-1 over ~10 h-170 kpc. The kinematics of the larger systems are generally consistent with orbital motions. Four galaxies are well described by rotating clumpy disks, and we extracted rotation curves out to radii >~10 h-170 kpc. One or two galaxies exhibit signatures more consistent with mergers. Analyzing all 14 galaxies in the framework of rotating disks, we infer mean inclination- and beam-corrected maximum circular velocities of vc~180 /-90 km s-1 and dynamical masses from ~0.5 to 25×1010 h-170 Msolar within r1/2. The specific angular momenta of our BM/BX galaxies are similar to those of local late-type galaxies. Moreover, the specific angular momenta of their baryons are comparable to those of their dark matter halos. Extrapolating from the average vc at 10 h-170 kpc, the virial mass of the typical halo of a galaxy in our sample is 1011.7 /-0.5 h-170 Msolar. Kinematic modeling of the three best cases implies a ratio of vc to local velocity dispersion vc/sigma~2-4 and, accordingly, a large geometric thickness. We argue that this suggests a mass accretion (alternatively, gas exhaustion) timescale of ~500 Myr. We also argue that if our BM/BX galaxies were initially gas-rich, their clumpy disks would subsequently lose their angular momentum and form compact bulges on a timescale of ~1 Gyr.