I'm confused of what you mean.
I suppose you understand that the recaptcha shortcode is to be added to the contact form 7 form, just in the textarea on the left where you generate the tag and not to be used directly on a post/page/text widget.
What you have to add to your post/page/text widget is the shortcode provided by contact form 7 that is something like:
[contact-form-7 id="211" title="Contact Form 1"]
After you have done that, a contact form should appear in the post, page or text widget where you added that shortcode. And if that form includes a recaptcha in its configuration then the recaptcha should appear either (NOTE: the recaptcha is only shown to unregistered users).
If you are doing it this way and it fails I suggest you try to first use a contact form 7 without recaptcha to let me know if it is BWP recaptcha extension the one that is breaking your contact form or just contact form 7 is not working for you.