I don't know, if the Rams keep winning, Bradford has a shot. It's been mentioned, but 4 weeks in is way too early.
Here's one site that's betting Jahvid Best is getting it.
2010 NFL Offensive Rookie of the Year Odds
902 Arrelious Benn +1500
903 Ben Tate +600
904 Brandon LaFell +2200
907 CJ Spiller +800
909 Dexter McCluster +1000
910 Dez Bryant +500
912 Emmanuel Sanders +1500
914 Golden Tate +1200
915 Jahvid Best +650
916 Jermaine Gresham +1500
917 Jimmy Clausen +1000
918 Jordan Shipley +2000
919 Montario Hardesty +1500
920 Rob Gronkowski +1500
922 Ryan Mathews +500
923 Sam Bradford +800
925 Tim Tebow +2000
926 Toby Gerhart +1500
928 Field +800
Another list, giving odds that Ryan Matthews or Dez Bryant are the best bets.
If the Rams can go 500 or better, I think Bradford has a shot, especially if the other top rookie teams go worse.