late Middle English: from French exorciser or ecclesiastical Latin exorcizare, from Greek exorkizein, from ex- 'out' + horkos 'oath'. The word originally meant 'conjure up or command an evil spirit'; the specific sense of driving out an evil spirit dates from the mid 16th century
Exorcise can also be spelled exorcize: both are correct.
Do not confuse exorcise with exercise. Exorcise means 'drive out an evil spirit' (a magic formula used to exorcise evil spirits), whereas exercise means 'carry out physical activity to get fitter' (she exercised every day) or 'use a right or power' (control is exercised by the Council).