We have measured the intensity of the cosmic microwave background (CMB) at a frequency of 7.5 GHz (wavelength 4.0 cm) using a ground-based, total power radiometer calibrated at the antenna aperture by an external cryogenic reference target. The radiometer measured the difference in antenna temperature between the reference target and the zenith sky from a dry, high-altitude site. Subtraction of foreground signals (primarily atmospheric and galactic emission) measured with the same instrument leaves the CMB as the residual. The radiometer measured the atmospheric antenna temperature by correlating the signal change with the air mass in the beam during tip scans. The small galactic signal was subtracted based on extrapolation from lower frequencies and was checked by differential drift scans. The limiting uncertainty in the CMB measurement was the effect of ground radiation in the antenna sidelobes during atmospheric measurements. The thermodynamic temperature of the CMB at 7.5 GHz is 2.60 ± 0.07 K (68% confidence level).