We present the results of a search for new members of the Taurus star-forming region using the Infrared Array Camera (IRAC) aboard the Spitzer Space Telescope}. With IRAC images of 29.7 deg^2 of Taurus at 3.6, 4.5, 5.8, and 8.0 um, we have identified sources with red mid-infrared colors indicative of disk-bearing objects and have obtained optical and infrared spectra of 23 of these candidate members. Through this work, we have discovered 13 new members of Taurus, two of which have spectral types later than M6 and thus are likely to be brown dwarfs according to the theoretical evolutionary models of Chabrier and Baraffe. This survey indicates that the previous census of Taurus has a completeness of ~80% for members with disks. The new members that we have found do not significantly modify the previously measured distributions of Taurus members as a function of position, mass, and extinction. For instance, we find no evidence for a population of highly reddened brown dwarfs (A_K~2) that has been missed by previous optical and near-infrared surveys, which suggests that brown dwarf disks are not significantly more flared than disks around stars. In addition to the new members, we also present IRAC photometry for the 149 previously known members that appear within this survey, which includes 27 objects later than M6.
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