v1.1 of AffiliateWP introduced the [affiliate_registration] shortcode. This shortcode allows you to place a registration form on any page.
In order for the registration form to appear on the page, Allow affiliate registration must be enabled from Affiliates → Settings → Misc.
If you'd like to redirect your affiliates after they register, use the redirect parameter of the shortcode:
Note: You will not see this form if you are already a registered affiliate.