Robson was admitted as a Solicitor on 4 June 1930 and practised with his father at Robson & Cowlishaw. He married Lesley Alison Martin in 1931 at St Stephen's Presbyterian Church, Sydney and had two sons. When sitting United Australia Party (UAP) MP William Foster died in office, Robson stood as an Independent UAP candidate at the resulting by-election in Foster's vacated Legislative Assembly seat of Vaucluse. At the by-election on 29 August 1936, he emerged successful, with 62.63% of the vote, becoming the third generation of his family to serve in the NSW Parliament.