Yes you can, although only if you raise federal constitutional arguments, or other arguments based on federal law - if your only argument is that the state cour

Yes you can, although only if you raise federal constitutional arguments, or other arguments based on federal law - if your only argument is that the state court got state law wrong, SCOTUS must reject it. Direct appeal is from the highest court in the state directly to SCOTUS, bypassing the rest of the federal courts. There is also indirect/collateral appeal, in which you aren’t appealing the state case, you are launching a new federal case as a habeas corpus petition or 42 USC 1983 civil suit.