The absolute cross section of the ³H(α,γ)⁷Li reaction has been measured for 50 ≤ E_(c.m.) ≤ 1200 keV. Specially prepared Ti-³H targets were bombarded with an α⁺ beam, and γ rays were detected using an 85% high-purity germanium detector. Total S-factors and the branching ratios for radiative capture to the two final bound states are reported for the entire energy range. Angular distributions of the capture γ rays were measured for nine energies in the range 115 ≤ E_(c.m.) ≤ 1200 keV. Legendre coefficients extracted from fits to the angular distributions are also reported. The preparation and characterization of the radioactive Ti-³H targets are discussed.This experiment is motivated by models of big-bang nucleosynthesis, which require the ³H(α,γ)⁷Li reaction rate for computing the primordial ⁷Li abundance. Our results have considerably smaller uncertainties and reach lower energies than previous experiments. For E≤ 150 keV, we find the S-factor to be considerably smaller than indicated by previous experiments. The measured branching ratio is found to be approximately energy independent, with a value of 0.45. The energy dependence of the measured S-factors is in agreement with existing theoretical calculations. The new results are used to calculate the thermonuclear reaction rate for temperatures below 10 GK.