We have obtained estimates of the solar internal rotational velocity from measurements of the frequency splittings of p-mode oscillations. Specifically, we have analyzed a 10-day time series of full-disk Dopplergrams obtained during July and August 1984 at the 60-Foot Tower Telescope of the Mt. Wilson Observatory. The Dopplergrams were obtained with a Na magneto-optical filter and a 244 × 248-pixel CID camera. From the time series we computed power spectra for all of the prograde and retrograde sectoral p-modes from ℓ = 0 to 200 and for all of the tessaral harmonics up to ℓ = 89. We then applied a cross-correlation analysis to the resulting sectoral power spectra to obtain estimates of the frequency splittings. From ℓ = 4 to ℓ = 30 we obtained a mean value of the frequency spitting of roughly 450 nHz (sidereal) in close agreement with most previously published results, while from ℓ = 40 to ℓ = 140 we obtained a mean value of about 470 nHz. We believe that the latter value is slightly higher than the surface rotational splitting of 461 nHz because of possible confusion due to the temporal sidelobes introduced by the day/night observing cycle. Confirmation of this possibility will have to await our computation of tesseral power spectra for degrees greater than our current limit of 89. Finally, for degrees between 140 and 200, the frequency splittings are indistinguishable from the surface rotation rate.