Is it acceptable to ask another faculty member from different department to review my paper prior to submission to a journal? I am a PhD student in Civil and Environmental Engineering and have just finished writing a paper which contains a statistical details. Is it acceptable to ask a faculty member in the statistics department in my university to revise my paper before submitting it to a journal to get it published?
Of course, as Enthusiastic Student says, you should check with your co-authors before sharing your unpublished work with anyone.  Once that is done, you can certainly ask.

Statisticians are very often asked to consult on the use of statistics in papers from other areas.  So it's possible that your institution has some system in place for such requests.  You should check with your advisor and/or other people who have done this before.  For example, some statistics departments have a "consulting pool" of graduate students who are available for jobs like this.

Some statisticians may only be interested if they would be doing enough work to qualify for co-authorship on the paper (see When does a statistical consultant become a co-author or collaborator? as linked by Stephan Kolassa).  Or, they may want to be paid.