Titan's geometric albedo varied noticeably from 1972 to 1978, in phase with variations in solar activity [Lockwood and Thompson, 1979>. We carry out a series of radiative transfer and aeorsol formation calculations in order to demonstrate the feasibility of the following scenario for these secular brightness changes: solar activity changes, especially in the UV output of the Sun, result in alterations to the mass production rate of aerosols in Titan's atmosphere, which lead to modifications of their microphysical properties. The latter, in turn, cause the albedo to vary. Current estimates of the change in the solar UV radiation below the dissociation limit of methane imply alterations to the mean radius of the aerosols over an 11-yr solar cycle that are consistent in sign and magnitude with those required to explain the observed secular brightness changes.