Croshaw is believed to be from the Crashaw family of Crawshawbooth, Lancashire, England; his parentage and date of birth are not known. He arrived in Jamestown, Virginia on the "Mary & Margrett", with the Second Supply in September 1608. It is assumed, his wife came over on the "Bona Nova" in 1620, however, she is not listed on the ships passenger rolls of the Bona Nova during any of its travels from London to Virginia. And, there has never been a reference to Captain Rawley Crashaw's wife's name in land deeds or the 1623 Census, it is also assumed she was likely dead by 1623. He was a member of the Virginia Company of London in 1609 and was still listed as an adventurer in the Company in both 1618 and 1620. He was one of the authors of the complimentary verses prefixed to "The General History of Virginia, New England, and the Summer Isles" (1624) of John Smith of Jamestown.