The standard pronunciation of C before the vowels I and E (occurring, for instance, in words "innocente" and "abbraccio") is /tʃ/ . However, I am watching a movie which takes place in Rome and everyone seems to pronounce it /ʃ/ instead. Does this pronunciation belongs to the Roman accent?
Yes, it is. Note that “ci”/“ce” is only pronounced like this after a vowel. So macello is pronounced /maʃel:o/, while cena or pancia are pronounced as in standard Italian.
This sound is sometimes written as “sc” (for instance in Belli's sonnets), but pay attention to the fact that “sc” denotes in standard Italian the geminated sound /ʃ:/, rather than /ʃ/. In other words, pece (in standard Italian), pece (in Roman dialect or regional Italian) and pesce have three different pronunciations.