The 33-year-old made 38 appearances this season and scored two goals after moving to Fratton Park from Millwall.
His campaign came to a premature end, however, after suffering a fractured cheekbone last month.
Robinson wrote on Twitter: “So happy to receive this from a brilliant group of lads, thank you!!”
Goalkeeper Paul Jones came second in the vote while defender Jack Whatmough was named young player of the year.