Add a subscribe/sign-up checkbox to Contact Form 7 plugin forms.

You can use the Newsletters – Contact Form 7 Subscribers extension plugin by Tribulant Software to do just that!

It will allow you to gather email/newsletter subscribers from WordPress Contact Form 7 plugin forms into the WordPress Newsletter plugin with ease.

It is a free extension plugin but the Newsletter plugin itself is premium. You can try out the Newsletter plugin LITE version though! The extension works with the LITE version too, no problem.

Capture email/newsletter subscribers from your Contact Form 7 plugin forms into the popular Newsletter plugin.

Source: WordPress Newsletter Plugin – Contact Form 7 Subscribers