To implement recaptcha in my website.
One option is google API . But for that i need to signup with domain name to get API key.
Is there any other way we can do it ?
You don't necessarily need a domain name to sign up, per se.
They have a concept of a "global key" where one single domain key would be used on several domains. When signing up, select the "Enable this key on all domains (global key)" option, and use a unique identifier (domainkey.abhilasha.com) and this will be fine, you can use the key from any domain in the end.