Actually he is running for president on the Republican ticket. And it really doesn't matter anymore as the differences between the two beltway country clubs are all but inconsequential.
Btw, we are electing a President, not a Republican or Democrat.
If I can be honest, considering what the R's and D's have done to America for 30+ years, few give a s**t about party.
Democrats destroy
Republicans allow everything fall apart
That about sums up my contrast on both partys.