I was lead to this paper from the footnotes of Ken Shoemake's 1985 paper on quaternions for flight-simulator animation. Although not the earliest, the following paper is one of the earliest mentions of quaternions in the context of computers. The earliest is by current (as of 2023) UCSD professor George Backus when he was a student at the University of Chicago in 1951. And in this context, computer refers not to computers as we know them now but analog computers.

Quaternion Parameters in the Simulation of a Spinning Rigid Body - E. E. L. Mitchell, A. E. Rogers.pdf 1968

Animating Rotation with Quaternion Curves - Ken Shoemake 1985

On the Use of Quaternions in Simulation of Rigid-Body Motion - Alfred C. Robinson 1958