High-resolution measurements of the pure rotational absorption spectrum of CO in its ground state are reported for the range J" = 5-37. A least-squares fit to this data set, augmented by previous microwave measurements of the J" = 0.4 rotational transitions by other workers, determined the following accurate values for the molecular constants (1 sigma errors of the last digits in parentheses): B0 = 57635.96826(12) MHz, D0 = 0.18350552(46) MHz, H0 = 1.7249(59) x 10(7) MHz, and L0 = -3.1(23) x 10(-13) MHz. A table of calculated CO rotational frequencies is given for the range J" = 0-45; these frequencies are accurate to less-than-or-equal-to 10 kHz (2-sigma) for J" less-than-or-equal-to 28.