For the first time, we present the low-mass function of the entire young star cluster Sigma Orionis (3 Myr, 352 pc, no internal extinction) from 0.25 Msun through the brown dwarf regime down to 3-4 Mjup in the planetary-mass domain. We have used VISTA Orion data (ZYJHKs) in the magnitude interval J= 13 - 21 mag (completeness at J = 21.0 mag, Z = 22.6 mag, and 10 Mjup). Combined with Spitzer/IRAC (3.6 and 4.5 micron) and optical images (Iz-band) from our archives has allowed us to identify over 200 cluster low-mass member candidates in an area of 0.79 deg2, i.e., uncovering most of the cluster area. All of these objects have colors compatible with spectral types M, L, and T, i.e., Teff = 3000-1000 K. 23 of them are new planetary mass candidates in the Sigma Orionis cluster, thus doubling the number of cluster planetary mass objects known so far. By considering the Mayrit catalog, we have "extended" our mass function from 0.25 Msun up to the high-mass stars (O-type) of the cluster, covering four orders of magnitude in mass.