We have conducted a study of debris disks around F stars in order to explore correlations between rotation, stellar winds, and circumstellar disks. We obtained new 24 μm photometry from the Multiband Imaging Photometer for Spitzer (MIPS) camera for a sample of 188 relatively nearby F dwarfs with various rotation rates and optical colors, and combined it with archival MIPS data for 66 more F stars, as well as Wide-field Infrared Survey Explorer data for the entire sample, plus 9 more F stars. Based on the objects' Ks -  and [3.4] -  colors, we identify 22 stars in our sample as having 22 and/or 24 μm excesses above our detection limit, 13 of which are new discoveries. Our overall disk detection rate is 22/263, or 8%, consistent with previous determinations of disk fractions in the solar neighborhood. While fast-rotating stars are expected to have strong winds capable of efficiently removing dust, we find no correlation between rotational velocity and infrared excess. Similarly, we find no significant difference in excess detection rate between late-type F stars, which have convective surfaces, and early-type F stars, which have fully radiative envelopes. However, the essentially unknown range of ages in this sample may be washing out any effects relating rotation, winds, and disks.