We report the rotation period of RX J1845.5-3750, a possible binary, weak-line T Tauri star at the extreme western edge of the Corona Australis star-forming region. The determination of the rotation period of young low-mass stars of different ages is fundamental for the understanding of the angular momentum evolution in pre-main-sequence stars, which is a debated issue. We also report a sudden drop in brightness, which is most likely due to a change in the cool spot(s) parameters resulting from rearrangements in the stellar magnetic field, or it could indicate that the secondary is a classical T Tauri star with a variable accretion rate. In a plot of lithium (6708 Å) equivalent width versus effective temperature, RXJ1845.5-3750 is very near the Pre-Main Sequence / Zero Age Main Sequence border.