Subscribers to my blog – adding

I recently added a subscriber button to my blog but it looks like I can only add each email individually.

I have been building an email list since 2010 and it consists of over 300 clients.

Is there a way to mass email all of these clients from wordpress/jet pack for them to subscribe to my blog.

It could take me hours to individually plug in each email manually. There has to be a way to upload all 300+ emails and from there they can decide to subscribe or not.

Thanks