Here you go:
regex domainGoogle "www\.google\.com\/recaptcha\/api\/verify"
access-list sleepy-google permit tcp host any eq 80
class-map type regex match-any GoogleCM
match regex domainGoogle
class-map httptraffic
match access-list sleepy-google
policy-map type inspect http http_inspection_policy
class GoogleCM
log
policy-map dmz-policy
class httptraffic
inspect http http_inspection_policy
service-policy dmz-policy interface dmz
This wouldn't work however if Google captcha verify page uses HTTPS (as HTTPS is encrypted session and the URL is encrypted within the HTTP), hence won't be able to use REGEX to allow it through.