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.