Try the Nam Myoho Rengi Kyo buddhist chant. I light a candle and use prayer beads to keep count. I reflect on the meaning of the chant as I sing it (which is very powerful, so definitely research it). I'll do it for up to 15min at a time.
You can find it on youtube here:
Personally, I've also found relief from anxiety from singing cherokee prayers/songs too. But uplifting repetitive chant sung (not just spoken) itself is the key. It's very soothing and causes your breathing to be deep with slow exhale and rhythmic which has an effect on the brain to stimulate "good chemicals". Doing it at least once a day (especially right when you wake up) is a great way to set your day off right in a good state of mind and calmness.
I have GAD (general anxiety disorder) due to a heart valve defect (MVP) so I will never get rid of it, I can only find ways to control it. I refuse to use medication for it, it's my body and I'm the master of my body! The mind is a powerful thing, we have to take control of it, or it will take control of us. Don't forget that, you're in control.