To add a Call-To-Action button to the header you simple need to add an extra menu item under the WordPress Menus page and assign a Custom CSS class to the menu. 

In the screencast above you can see that the assigned class is cta-button to the additional menu item. If you don't see the Custom CSS file make sure it's enabled under the Screen Options.

Now you only need to add the following code to the Custom CSS field in your WP Dashboard > Divi Theme Options > General Settings

.cta-button {
    border: 1px solid red;
    border-radius: 19px;
    background: blue;
    box-shadow: 0px 0px 12px 3px violet;
    transition: all .3s 0s;
}

.cta-button a {
    padding: 18px !important;
    color: white !important;
}

.cta-button:hover {
    transform: scale(1.1);
    transition: all .2s 0s;
}

That's it! You can play with all the values in the code to customize the button the way you need. You can see the final result in the screencast below:

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