Tolkien doesn't give the exact date of the Orcs' attack, but we can calculate it from associated information. We know that Isildur set out on Yavannië 5 (by the calendar of Númenor), and that he was attacked on the thirtieth day of his journey. According to the King's Reckoning, that would be Narquelië 4. That translates onto the Shire Calendar as the fourth day of Winterfilth (October), or onto a modern calendar as 25 September.