Have you tried melatonin before you go to bed? It really works for me and got me through a rough period of waking up with anxiety. It was always between 3-4 a.m. for me, too, and as others have mentioned there is a biological reason for that. Magnesium and potassium are essential too, so make sure you have a good diet and good sleep habits.
Other than the physical, as others have also mentioned, the Rosary helps tremendously. I’ve heard Our Lady referred to as Our Lady of Good Sleep, and this comforts me a lot. It was our mothers who rocked us to sleep when we were children! If I don’t fall back to sleep saying the Rosary (90% of the time), I assume God woke me up to pray for someone, so I offer it up.
I’ve also found that lack of sleep for a short period is not the end of the world. On those draggy mornings when you just want to go back to bed, mind over matter works. On days I think will be horrible because I’ve had no sleep, I often am surprised that things were just fine. My point is, when you wake up at 3:00 and feel anxious, just don’t sweat it. It will be ok!