We present a measurement of the star formation history of Sextans A, based on WFPC2 photometry that is 50% complete to V = 27.5 (MV ~ +1.9) and I = 27.0. The star formation history and chemical enrichment history have been measured through modeling of the color-magnitude diagram (CMD). We find evidence for increased reddening in the youngest stellar populations and an intrinsic metallicity spread at all ages. Sextans A has been actively forming stars at a high rate for ~2.5 Gyr ago, with an increased rate beginning ~0.1 Gyr ago. We find a nonzero number of stars older than 2.5 Gyr, but because of the limited depth of the photometry, a detailed star formation history at intermediate and older ages has considerable uncertainties. The mean metallicity was found to be [M/H] ≈ -1.4 over the measured history of the galaxy, with most of the enrichment happening at ages of at least 10 Gyr. We also find that an rms metallicity spread of 0.15 dex at all ages allows the best fits to the observed CMD. We revisit our determination of the recent star formation history (age ≤ 0.7 Gyr) using blue helium-burning (BHeB) stars and find good agreement for all but the last 25 Myr, a discrepancy resulting primarily from different distances used in the two analyses and the differential extinction in the youngest populations. This indicates that star formation histories determined solely from BHeB stars should be confined to CMD regions where no contamination from reddened main-sequence stars is present.