This one certainly should be marked 'of disputed antiquity'. But despite its decidedly blocky shape I take encouragement from the Aberdeen County Council Sites and Monuments Record here which suggests it's possible the nearby Langstone and this stone were once part of a single monument. It also explains the crustacean-unrelated origin of the name, that the stone was on the boundary of land belonging to a burgess of Aberdeen in the 14th century, John de Crabbe.
Volume 19 of the 1797 statistical account says
In September 1644, during the time of the civil wars, the Marquis of Montrose, with an army of about 2000 men, having approached the town of Aberdeen, and summoned it to surrender to him, the Magistrates, after advising with Lord Burleigh, who then commanded in the town a force nearly equal in number to the assailants, refused to give up the town, upon which a battle ensued within half an English mile of the town, at a place calle the Crab-stone, near to the Justice-mills, where Montrose prevailed, and many of the principal citizens were killed.
This was the 'Battle of Justice Mills' and it all sounds very unpleasant. There is a well just down the road (the Hardgate Well) which is associated with the battle and was said to have run red with the blood (though the Canmore record puts this idea down to recent folklore). There was another battle here the previous century, the 'Battle of Craibstone' on 20th November 1571, part of a long-running feud between the Forbes and Gordon clans.