Can I pursue computer science engineering from BIT, Mesra with 44923 rank under OBC category?

That depends upon whether you are a student from the home state or a candidate from other than home state. You see, there is a reservation for the students who belong to the home state I.e, Jharkhand itself. If you want to lookup the opening and closing ranks for 2016 use this: http://josaa.nic.in/R

No, you can't get Computer science engineering at this rank . Cutoff for CSE at BIT Mesra is high. You may get polymer technology or biotechnology at this rank (Assuming you to be a general category student).