Is it difficult to be fully funded for PhD in STEM field in US? I have reached out to some professors for my research interest.  I am wondering whether it is difficult to be fully funded for my PhD program in civil engineering. 
Is it appropriate to ask the professors whether I will be fully funded for my PhD?
Yes it is appropriate to ask, both for the program and the individual professors. Hopefully you ask other important and research-related questions at the same time, but funding is not a taboo topic for a prospective student, and it should be one of the keys to your decision if you are accepted to multiple programs.

Many programs (in STEM in general, can't speak to civil engineering in particular) offer fully-funded programs (tuition+a stipend) for PhDs (less often for masters), but there may be limits (for example you may be guaranteed for only 5-6 years, and if it takes longer you might still get funding just not guaranteed), and you almost certainly won't be free to do whatever you want: you may be required to teach ("TA") whether you want to or not, you may be required to join a lab that has funding available ("RA"), even if that lab was not your first choice otherwise, or you might have to do other work for another lab/group that isn't directly related to your research (as an RA or PA). Fellowships or traineeships are directly funding YOU and are the best source of funding but are often competitive and may cover only a short period of time.

"Fully funded" could include ANY combination of the above, so you should ask questions about the types of funding and not just a guarantee. Current students are also a great resource.