Yes, its possible for an SMSF to purchase cryptocurrency.
Key factors to be aware of:
The Trust deed of the SMSF specifically has to allow cryptocurrency assets;
It must form part of a documented Investment Strategy for the SMSF;
The SMSF must be able to prove the ownership and existence of the crypto for the independent audit of the fund - i.e. account MUST be in the name of the SMSF - some exchanges don't enable SMSF accounts to be registered (but more reputable Australian ones like CoinSpot, Independent Reserve etc do)
Consider how the crypto investments are to be administered and audited. If you make it challenging for the accountant and auditor it will increase your fees.