We report on a study of $W$ + photon production in approxmately 20 $pb^{-1}$ of $p-\bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV recorded with the Collider Detector at Fermilab. Our results are in good agreement with Standard Model expectations and are usedto obtain limits on anomalous CP-conserving $WW\gamma$ couplings of $-2.3 < \delta\kappa < 2.2$ for $\lambda = 0$ and $-0.7 < \lambda < 0.7$ for $\delta\kappa = 0$ at $95\%$ C.L. We obtaint the same limits for CP-violating couplings. These results provide limits on the higher order electromagnetic (EM) moments of the $W$ boson of $0.8 < g_W < 3.1$ for ${q_W}^e = 1$ and $-0.6 < {q_W}^e < 2.7$ for $g_W = 2$ at $95\%$ C.L.