There are many WordPress plugins that let you manage your email subscription. But overall this is not recommended, mainly because it creates a heavy load on the server. What will inevitably create a problem with the hosting service.
In my experience, it is advisable to work with professional external services. For various reasons among which I highlight:
- They make sending mail (high load)
- They have good design tools
- They know a lot about how to make your mails do not fall as SPAM
These services have different forms of design that attach easily with WordPress themes. An example is Mailchimp.com. But there are others.
This article can help you with more information. I hope you find it useful.
WPBeginner - Why You Should Never Use WordPress to Send Newsletter Emails