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 keV) < 1E44 erg/sec. 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.