Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m. However, despite numerous experimental attempts, clear signatures of fractional statistics remain elusive. Here we experimentally demonstrate abelian fractional statistics at filling factor ν = 1/3 by measuring the current correlations resulting from the collision between anyons at a beam-splitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions. arXiv:2006.13157v1 [cond-mat.mes-hall]