A man has been charged with four counts of assault after four women were allegedly attacked on an Adelaide train line.

South Australian police said the four women were travelling separately between Kilburn and Adelaide, when they were all randomly assaulted by a man unknown to them who allegedly "punched, slapped, pushed, spat at and verbally abused" them.

The women were travelling on the Adelaide-bound Gawler train line on Sunday morning, just before 9am.

Police said the 47-year-old accused from Salisbury jumped the exit barrier as the train arrived in Adelaide and ran towards the Adelaide Oval where he was caught and arrested.

He has been issued with a three-month ban on using public transport and has been bailed to appear in the Adelaide Magistrates Court in August.

None of the women who were assaulted required medical treatment.

Police are investigating, and have asked members of the public who witnessed the attack, or have footage of the incident to contact Crime Stoppers.