Visiting US with criminal conviction

[ringer]

My cousin is an Australian citizen and has a criminal conviction from 13years back when he was applying for loan to buy a car, that car was used to get the loan for many people before, so he got 18months good behaviour bond but no jail,
now he wants to visit US with me(I m also Australian Citizen), i m just wondering if he needs to apply the visa beforehand? or whether he can visit US on ESTA?
as we tried getting this police check done through AFP and as the conviction is already spent so there is no record for it and my cousin also has got no paper record for that event,
Please advise.