Aims.Active Galactic Nuclei are known to be variable throughout the electromagnetic spectrum. An energy domain poorly studied in this respect is the hard X-ray range above 20 keV. Methods.The first 9 months of the Swift/BAT all-sky survey are used to study the 14-195 keV variability of the 44 brightest AGN. The sources have been selected due to their detection significance of >$10 \sigma$. We tested the variability using a maximum likelihood estimator and by analysing the structure function. Results.Probing different time scales, it appears that the absorbed AGN are more variable than the unabsorbed ones. The same applies for the comparison of Seyfert 2 and Seyfert 1 objects. As expected the blazars show stronger variability. 15% of the non-blazar AGN show variability of >$20\%$ compared to the average flux on time scales of 20 days, and 30% show at least $10\%$ flux variation. All the non-blazar AGN which show strong variability are low-luminosity objects with $L_{(14{-}195\,\rm~keV)} < 10^{44} \rm \, erg \, s^{-1}$ Conclusions.Concerning the variability pattern, there is a tendency of unabsorbed or type 1 galaxies being less variable than the absorbed or type 2 objects at hardest X-rays. A more solid anti-correlation is found between variability and luminosity, which has been previously observed in soft X-rays, in the UV, and in the optical domain.