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Laser light with photon energy near the band gap of GaAs and in Laguerre-Gaussian modes with different amounts of orbital angular momentum was used to produce photoemission from unstrained GaAs. The degree of electron spin polarization was measured using a micro-Mott polarimeter and found to be consistent with zero with an upper limit of ~3% for light with up to + or -5h of orbital angular momentum. In contrast, the degree of spin polarization of 32.3 + or - 1.4% using circularly polarized laser light at the as the same wavelength, which is typical for bulk GaAs photocathodes.