There are several plugins which claim to do that, here's one for example: https://wordpress.org/plugins/wp-music/
You can also use the standard audio player which comes with WP. Just set the loop and autoplay attributes to on:
[audio src="..." loop="on" autoplay="on"]
You can even hide it in the background:
<div style="display: none">[audio src="..." loop="on" autoplay="on"]</div>