1. There are several plugins which claim to do that, here's one for example: https://wordpress.org/plugins/wp-music/
or
2. You can also use the standard audio player which comes with WP. Just set the loop and autoplay attributes to on:
[audio src="here paste the music file URL" loop="on" autoplay="on"]
You can even hide it in the background:
Please paste the code below in your Text tab. Please note that you need to add the URL of your music file uploaded previously in the Media Library.
<div style="display: none">[audio src="here paste the music file URL" loop="on" autoplay="on"]</div>
