The Lancashire paceman has been hastily picked as a possible replacement for team-mate Finn, who has reported suffering from a stiff back.
Anderson was in the England side which suffered a seven-wicket defeat to the Proteas on Wednesday as the one-day international series ended tied at 2-2.
The 30-year-old has not played for England in the shortest form of the game since his appearance against South Africa in a match at Centurion in November 2009.
He is not part of the England squad for the ICC World Twenty20 which starts in Sri Lanka later this month.
The first Twenty20 takes place at Chester-le-Street on Saturday, September 8.
T20 squad: Stuart Broad (Nottinghamshire, captain), Jonny Bairstow (Yorkshire), Ravi Bopara (Essex), Tim Bresnan (Yorkshire), Danny Briggs (Hampshire), Jos Buttler (Somerset), Jade Dernbach (Surrey), Steven Finn (Middlesex), Alex Hales (Nottinghamshire), Craig Kieswetter (Somerset), Michael Lumb (Nottinghamshire), Eoin Morgan (Middlesex), Samit Patel (Nottinghamshire), Graeme Swann (Nottinghamshire), Luke Wright (Sussex)
World Twenty20 squad: Broad (Nottinghamshire) (captain), Bairstow (Yorkshire), Bopara (Essex), Bresnan (Yorkshire), Briggs (Hampshire), Buttler (Somerset), Dernbach (Surrey), Finn (Middlesex), Hales (Nottinghamshire), Kieswetter (Somerset), Lumb (Nottinghamshire), Morgan (Middlesex), Patel, Swann (both Nottinghamshire), Wright (Sussex)