Before I go over the mock draft, this is to assume that the Rams would not trade down and stay at pick #2
Round 1a: Jadaveon Clowney. Jeff Fisher loves a complete Defensive lineman and adding an potential elite defensive player is like winning the lottery. They can move Chris Long inside to be the 3-Technique DT since he excels as a 3-4 end or 3 technique DT in college.
Round 1b: CB Darqueze Dennard: The best physical cornerback out of Michigan State.
Round 2: OG/OT David Yankey: Jeff Fisher prefers versatile offensive lineman and Yankey is the best available at this spot
Round 3: QB AJ McCarron: The Rams need an upgrade to Kellen Clemens and AJ McCarron has played in a pro style offense which hastens the transistion to the NFL level. He is also a proven leader.
Round 4: CB E.J. Gaines he practically held Mike Evan to just 4 catches in 8 receiving yard. With that cover skills he can cover practically any receivers big or small. Rams can move him at Free Safety if needed
Round 5: OLB Denicos Allen - He's part of those very athletic Linebackers that stopped Ohio State from winning the Big Ten Championship he's the top candidate to replace Jo-Lonn Dunbar
Round 6: OT Justin Britt: Britt represented the Tiger offense on the SEC first-team, as he helped pave the way for an offense which was one of the most improved in the nation in 2013.
Round 7: BPA TE - Rams needed depth at TE since Mike McNiel will be a FA