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 insight 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 1,974 confirmed T Tauri members of various sub-regions 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 sub-populations 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.