We present a study of galaxies showing mid-infrared variability in data taken in the deepest Spitzer/MIPS 24 $mu$m surveys in the GOODS-South field. We divide the dataset in epochs and subepochs to study the long-term (months-years) and the short-term (days) variability. We use a $chi^2$-statistics method to select AGN candidates with a probability $leq$ 1% that the observed variability is due to statistical errors alone. We find 39 (1.7% of the parent sample) sources that show long-term variability and 55 (2.2% of the parent sample) showing short-term variability. That is, 0.03 sources $times$ arcmin$^{-2}$ for both, long-term and short-term variable sources. After removing the expected number of false positives inherent to the method, the estimated percentages are 1.0% and 1.4% of the parent sample for the long-term and short-term respectively. We compare our candidates with AGN selected in the X-ray and radio bands, and AGN candidates selected by their IR emission. Approximately, 50% of the MIPS 24 $mu$m variable sources would be identified as AGN with these other methods. Therefore, MIPS 24 $mu$m variability is a new method to identify AGN candidates, possibly dust obscured and low luminosity AGN, that might be missed by other methods. However, the contribution of the MIPS 24 $mu$m variable identified AGN to the general AGN population is small ($leq$ 13%) in GOODS-South.
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