Is there a reliable way to measure how difficult it is to be admitted to a PhD program? If I wanted to check how competitive it is to get into a school's PhD (or MS/PhD track) program, what should I look at? For undergraduate, I usually search for the incoming SAT/ACT scores and the acceptance rate, and I found that pretty reliable. Is there something like that for grad schools?
I am not aware of any absolute measure for this. However, you can have a general idea by: 


Some schools provide last year(s) statistics about their programs
(usually in the prospective student section). For example, program A
has attracted X number of applications and Y applications were
accepted.
Also, some programs have a fix limit (i.e. due to number of equipments available)  for number of applications to be accepted. 
Sometimes online admission results like the one in Grad Cafe
give you a sense on how strict the school is.