The Sony Xperia R1 has a microSDXC memory card reader. If your personal computer can also read that card type (Most notebooks are so-equipped), you should be able to save music files (The Sony R1 supports these formats: Yes) from your computer to a microSDXC memory card, and then, from the memory card to your Sony R1. Your owner's manual should tell you how to assign the musical file to your phone's main ringtone.
The Sony R1 is an Android phone and there are plenty of free ringtone apps such as MP3 Cutter, Zedge and more.
Since your Sony Xperia R1 is equipped with a sound recorder (also known as 'voice memo'), a very simple technique involves just putting your phone near your computer's speakers, playing whatever song, music or sound you would like as a ringtone, and recording it -- you can even use your voice, your child's voice or even your cat's 'meow!' Record it with your mobile and there you go! Unless that function was specifically blocked on the Sony R1, you should be able to navigate to the ringtones menu and choose your new recording as a ringtone. Of course, the quality may not be optimal but, after all, it's free!
More on free ringtones
Here are links to some of the 100% free ringtones (Sony R1-compatible) offered here at MartinsRingtones.com:
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