Accept what ? Commission Junction open for register and you will get instant approved. If your mean is accept by advertiser, it by many factors like your niche, traffic ...
All you need to do is verify your website with cj. Once its been verified then your account will be active.
you will get instantly approved ,but you may not get approved by the person who want you to complete offers.
CJ accepts the every registered users, but if you mean acceptance by advertisers, you should have some decent site and you won't be rejected by all advertisers, generally new and small advertisers or least advertisers accepts everyone of same niche quickly. Yesterday i have joined CJ.com and i got approved for more than 4 advertisers for three different sites.
Cj will approve you , but other advertisers within cj want a website that's attractive, high quality content in order to approve you. Some advertisers with affiliate programs may even want to see traffic! hope this helps.
When I was trying for some affiliates, CJ accepted me, but when applying to the affiliates, some are very picky on who they want. No matter what you offer them.