Most existing studies of the angular momentum evolution of young stellar populations have focused on the youngest (~1-3 Myr) T Tauri stars. In contrast, the angular momentum distributions of older T Tauri stars (~4-10 Myr) have been less studied, even though they hold key insights to understanding stellar angular momentum evolution at a time when protoplanetary disks have largely dissipated and when models therefore predict changes in the rotational evolution that can in principle be tested. We present a study of photometric variability among 1974 confirmed T Tauri members of various subregions of the Orion OB1 association, and with ages spanning 4-10 Myr, using optical time series from three different surveys. For 564 of the stars (~32% of the weak-lined T Tauri stars and ~13% of the classical T Tauri stars in our sample) we detect statistically significant periodic variations, which we attribute to the stellar rotation periods, making this one of the largest samples of T Tauri star rotation periods yet published. We observe a clear change in the overall rotation period distributions over the age range 4-10 Myr, with the progressively older subpopulations exhibiting systematically faster rotation. This result is consistent with angular momentum evolution model predictions of an important qualitative change in the stellar rotation periods starting at ~5 Myr, an age range for which very few observational constraints were previously available.