We investigate the nature of the long-period radial velocity variations in Alpha Tau first reported over 20 years ago. We analyzed precise stellar radial velocity measurements for Alpha Tau spanning over 30 years. An examination of the Halpha and Ca II 8662 spectral lines, and Hipparcos photometry was also done to help discern the nature of the long-period radial velocity variations. Our radial velocity data show that the long-period, low amplitude radial velocity variations are long-lived and coherent. Furthermore, Halpha equivalent width measurements and Hipparcos photometry show no significant variations with this period. Another investigation of this star established that there was no variability in the spectral line shapes with the radial velocity period. An orbital solution results in a period of P = 628.96 +/- 0.90 d, eccentricity, e = 0.10 +/- 0.05, and a radial velocity amplitude, K = 142.1 +/- 7.2 m/s. Evolutionary tracks yield a stellar mass of 1.13 +/- 0.11 M_sun, which corresponds to a minimum companion mass of 6.47 +/- 0.53 M_Jup with an orbital semi-major axis of a = 1.46 +/- 0.27 AU. After removing the orbital motion of the companion, an additional period of ~ 520 d is found in the radial velocity data, but only in some time spans. A similar period is found in the variations in the equivalent width of Halpha and Ca II. Variations at one-third of this period are also found in the spectral line bisector measurements. The 520 d period is interpreted as the rotation modulation by stellar surface structure. Its presence, however, may not be long-lived, and it only appears in epochs of the radial velocity data separated by $sim$ 10 years. This might be due to an activity cycle. The data presented here provide further evidence of a planetary companion to Alpha Tau, as well as activity-related radial velocity variations.
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