So the anawer to this is “Yes”.
Photons can oscilate “up and down” or rotate like a corkscrew. Those are called the linear and circular polarisations. We can measure it because is does stuff, they jiggle electric charges.
A photon is an oscillation of the electromagnetic field. Think of three arrows (vectors, if you know what those are). One points in the direction of the photon’s motion (well, sort of, they do spread everywhere evenly, but also sort of not. Quantum physics for you). The other two are 90 degrees to the first arrow and each other. So like a corner of a cube.
Those latter two represent the strength of the electric and magnetic fields. They’re the thing that oscillate. So they can just oscillate “up and down” along the direction of motion, like a standard sine wave. That’s linear polarization. By convention, the direction of polarisation is the direction of the electric field vector. You can tell if it’s that because we can make polarisation filters made of many parallel slits that will allow only that orientation through. Polarised filters are fun to play with, they do completely counterintuitive quantum things on a human scale (google three polarisation filter experiment).
But these perpendicular vectors of the electric and magnetic fields CAN be spinning clockwise or anticlockwise along the direction of motion, making a corkscrew shape instead. That’s circular polarization.
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