We present projected rotational velocities for 20 early-type (B8-A9) and 74 late-type (F2-M8) members of the ~5 Myr old Upper Scorpius OB Association derived from high dispersion optical spectra obtained with the High Resolution Echelle Spectrometer (HIRES) on Keck I and the Magellan Inamori Kyocera Echelle (MIKE) on the Magellan Clay telescope. The spectroscopic sample is composed of stars and brown dwarfs with infrared signatures of circumstellar disks, both primordial and debris, and non-excess sources of comparable spectral type. We merge projected rotational velocities, accretion diagnostics, and Spitzer Space Telescope Infrared Array Camera (IRAC) and Multiband Imaging Photometer for Spitzer (MIPS) 24 micron photometry to examine the relationship between rotation and circumstellar disks. The rotational velocities are strongly correlated with spectral type, a proxy for mass, such that the median vsini for B8-A9 type stars is: 195(+/-)70 km/s, F2-K4: 37.8(+/-)7.4 km/s, K5-K9: 13.8(+21.3/-8.2) km/s, M0-M5: 16.52(+/-)5.3 km/s, and M5.5-M8: 17.72(+/-)8.1 km/s. We find with a probability of >0.99 that M-type stars and brown dwarfs having infrared excess suggestive of circumstellar disks rotate more slowly than their non-excess counterparts. A similar correlation is present among F2-K9 type stars, but only at the ~97% confidence level. Among the early-type (B8-A9) members, rotational velocities of the debris-disk and non-disk populations are indistinguishable. Considering the late-type (F2-M8) stars and brown dwarfs, we find a low fraction of slowly rotating, non-excess sources relative to younger star forming regions, suggesting that most have spun up following disk dissipation. The few late-type (F2-M5) debris disk sources, which may be representative of stars that have recently dispersed their inner disks, are evenly divided between slow and moderate rotators.