Yes. There are various licences available to do with broadcasting music online – you can find out more here.
PRS for Music has a blanket licence with YouTube – so any music you upload is covered by that license. Often the easiest way to put music on your site is to put it on YouTube and either link or embed the video into your site – that way it will be covered the YouTube licence. Embedding is fairly easy to do – click on the ‘Share’ button below the video on YouTube – this will then give you a code to embed the video into another site).