No, please don't
First of all, I'd try to study and test if I need a captcha. And I mean, test it thoroughly. While Captcha are an obvious enhance in security, they have severe issues in terms of usability. see the docs below:
This is just a small sample, but it would be useful for you to read them so you understand the pros and cons. However, if you don't want to read those docs, I'll simplify it: captchas are extremely annoying and disturbing and they affect usability and conversions
So, what to do?
Of course, you can use other methods like honeypots, but if you decide that you want to use a captcha, you should be aware you're adding friction for the user, whether you need it or not, this is an objective fact. So, adding yet more friction is getting into the anti-pattern realm.
Think about this:
User enters password properly User enters wrong captcha
Now you delete the pass and user enters wrong password and correct
Now user has no idea what's going wrong, tries another pass
Another try with another pass?
At this point, if user is desperate, s/he will ask for a password remainder. Otherwise, s/he will simply abandon your site forever. Please note that the above is not a random flow, but a very common user flow. Also, if you're thinking in terms of security... well, you made the user enter all his passwords and variations. If this is a concern for you, you just provided a hacker with lots of REAL passwords.
Do NOT create friction. Never. Just use the smallest friction possible within the specs and always try to find alternatives. Thus, if the password is correct, just leave it and let the user deal with the captcha alone. And again: unless your need for captcha is really extreme (eg you need a great deal of security), look for alternatives