Rotate Photon Polarization: 90 Degrees?

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If I'm given a photon polarized at some unknown angle, can I rotate it by 90 degrees (or by an arbitrary angle)?
 
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Yes, although it may be difficult for a single photon.

There are lots of different ways of altering the polarization of a beam of light, generally. You could use a half-wave plate, or a birefringent medium, or a Faraday rotator, for example.
 
Individual photons have "helicity", which translates into circular polarization. So 'rotating' the photon will not change the polarization state.

Going over to the macroscopic description of polarization, with arbitrary polarization states, means that the light is now composed of a population of partially (mutually) coherent photons. Pure polarized light is completely coherent, randomly polarized light is incoherent. Descriptions of polarizers and retarders using photons is statistical in nature.

The polarization of light corresponds to spin, certain specially-prepared fields (Bessel beams, etc) of radiation possesses a property corresponding to angular momentum.
 

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