Résumé : We present new constraints on the merging rates of planetary-mass and asteroid-mass primordial black hole binaries using limits on continuous waves (quasimonochromatic, quasi-infinite duration signals) derived from an all-sky search for isolated compact objects in the first six months of the third observing run (O3a) of LIGO/Virgo. We calculate the merging rates of these binaries in a model-independent way, and convert them to constraints on the primordial black hole abundance with minimal modeling assumptions. Our results show that all-sky searches are sensitive to sources at most O(10 pc) away for systems with chirp masses of O(10-5 M⊙) at gravitational-wave frequencies around 30 Hz-40 Hz. These results also show that continuous-wave searches could in the future directly probe the existence of planetary-mass and asteroid-mass primordial black holes, especially those in binaries with asymmetric mass ratios. Furthermore, they demonstrate that new methods accounting for the full nonlinear gravitational-wave frequency evolution are needed to improve constraints on primordial black holes.