I read the Wiki page
https://en.wikipedia.org/wiki/Electron_cyclotron_resonance
as well as this answer here
and it describes a setup where one has a cyclotron which has a static magnetic field pointing up through the dees and there is an alternating high voltage across the dees. An alpha particle is attracted to a negatively charged plate so it moves towards the 'negative dee'. It moves in a circle because of the Lorentz force of the perpendicular magnetic field. When it gets around the semicircle, the voltage is flipped so now the particle jumps across and is accelerated from one dee to the other. I interpret this to mean that acceleration only happens when moving across one dee to the other. However, as the alpha particle is moving withing a dee, it is experiencing a force causing it to move circularly. Technically, the particle is being accelerated here too, but instead of acquiring linear momentum, it is acquiring angular momentum.
However, people smarter than me have said that alpha particles don't spin
Can the rotation of an alpha particle be measured?
Can someone enlighten me as to why alpha particles dont get angular momentum in a cyclotron?