We have derived the angular correlation function of a sample of 2096 sources detected in the ROSAT All-Sky Survey (RASS) Bright Source Catalogue, in order to investigate the clustering properties of active galactic nuclei (AGN) in the local Universe. Our sample is constructed by rejecting all known stars, as well as extended X-ray sources. Areas with |b|<30° and declination δ<-30° are also rejected owing to the high or uncertain neutral hydrogen absorption. Cross-correlation of our sample with the Hamburg/RASS optical identification catalogue suggests that the vast majority of our sources are indeed AGN. A 4.1σ correlation signal between 0° and 8° was detected with w(θ<8°)=2.5±0.6×10−2. Assuming a two-point correlation function of the form w(θ)=(θθ0)−0.8, we find θ0=0.°062. Deprojection on three dimensions, using Limber’s equation, yields a spatial correlation length of r0≈6.0±1.6 h−1 Mpc. This is consistent with the AGN clustering results derived at higher redshifts in optical surveys and suggests a comoving model for the clustering evolution.