It turns out the Minnesota Vikings, recent recipients of nearly $500 million in taxpayer subsidies (which was a terrible idea for reasons outlined here), lead the league in arrests since 2000.
My source is the USA Today NFL Player Arrest Database. I basically copied and pasted all the records into a text file, then ran a little bash one-liner to count the number of arrests by team:
jsaxton@home:/tmp$ cat arrests.txt | cut -f 2 | sort | uniq -c
12 ARI
18 ATL
23 BAL
18 BUF
19 CAR
28 CHI
43 CIN
28 CLE
14 DAL
40 DEN
17 DET
2 Free agent
17 GB
11 HOU
24 IND
24 JAC
7 JAX
30 KC
28 MIA
45 MIN
15 NE
20 NO
14 NYG
15 NYJ
19 OAK
14 PHI
21 PIT
26 SD
22 SEA
19 SF
12 STL
32 TB
33 TEN
20 WAS