We use the multi-epoch, mid-infrared Spitzer Deep Wide-Field Survey to investigate the variability of objects in 8.1 deg(2) of the NOAO Deep Wide Field Survey Bootes field. We perform a Difference Image Analysis of the four available epochs between 2004 and 2008, focusing on the deeper 3.6 and 4.5 mu m bands. Out of 474,179 analyzed sources, 1.1% meet our standard variability selection criteria that the two light curves are strongly correlated (r > 0.8) and that their joint variance (sigma(12)) exceeds that for all sources with the same magnitude by 2 sigma. We then examine the mid-IR colors of the variable sources and match them with X-ray sources from the XBootes survey, radio catalogs, 24 mu m selected active galactic nucleus (AGN) candidates, and spectroscopically identified AGNs from the AGN and Galaxy Evolution Survey (AGES). Based on their mid-IR colors, most of the variable sources are AGNs (76%), with smaller contributions from stars (11%), galaxies (6%), and unclassified objects, although most of the stellar, galaxy, and unclassified sources are false positives. For our standard selection criteria, 11%-12% of the mid-IR counterparts to X-ray sources, 24 mu m AGN candidates, and spectroscopically identified AGNs show variability. The exact fractions depend on both the search depth and the selection criteria. For example,12% of the 1131 known z > 1 AGNs in the field and 14%-17% of the known AGNs with well-measured fluxes in all four Infrared Array Camera bands meet our standard selection criteria. The mid-IR AGN variability can be well described by a single power-law structure function with an index of gamma approximate to 0.5 at both 3.6 and 4.5 mu m, and an amplitude of S-0 similar or equal to 0.1 mag on rest-frame timescales of 2 yr. The variability amplitude is higher for shorter rest-frame wavelengths and lower luminosities.