W boson + QCD Jet events, produced in 1.8 TeV proton-antiproton collisions and measured by the Collider Detector at Fermilab (CDF), were used to measure the center-of-mass production angle of the W + jet system, and were also used to place limits on the production of excited quark states. The center-of-mass production angular distribution agrees well with leading order and next-to-leading order QCD predictions. Excited quark states were searched for in the reaction q + g {yields} q* {yields} q + W. Upper limits on the q* cross section, as a function of the q* mass, are shown. Comparison with a theoretical prediction for q* production excludes excited quark states with a mass in the range 150--530 GeV/c{sup 2}, at 95% confidence.