Hi

A non commerce background can pursue CA course other than fine arts students.you have to register yourself for CA foundation exam to get entry in CA course from their official website www.icai.org.the exams generally conducted in May and November.after clear intermediate exam or foundation you move to other stage called IPCC It contains two modules you can give both modules together or separately its upto your choice.if you clear one module and complete 8 months of study course you are eligible for registering yourself for 3 years practical training.after completion of training and passing in two modules you can go for CA final which is very crucial stage.after clearing CA final you become member of icai.

I suggest you to choose CA if you are interested otherwise it may difficult for you to pursue course because it has more of practical knowledge in accounting which basics taught in intermediate level. however many non commerce background become CA and ace in it.

Best wishes for your future..