What a good question, I’d never thought to consider it.
Well, the OED says that it comes from the noun ‘park’ Cf. Middle French, French parquer ‘to put (animals) in an enclosure’ (1380), ‘to fortify (a camp)’ (1470), ‘to establish oneself in a strategic position’ (1488), ‘to set up camp’ (1495).
And here’s a citation referring to wagons:
1846 G. B. MCCLELLAN Mexican War Diary Nov. (1917) 10 To the left of the sand hills in front are a number of wagons parked, to the left of them a pound containing about 200 mules.
So there seems to be a nice logical set of semantic leaps: from enclosing animals in a park, to setting up a camp, to positioning wagons, to positioning other vehicles.