You can, for a fee:
Permit and Alligator Trapping License for Florida Residents (includes 2 CITES tags for the harvest of 2 alligators): $272.00
Permit and Alligator Trapping License for Non-Residents (includes 2 CITES tags for the harvest of 2 alligators): $1,022.00
Permit and Alligator Trapping License for Resident Disability Hunt/Fish License Holders (includes 2 CITES tags for the harvest of 2 alligators): $22.00
Permit for 2 CITES tags (for customers who already have an Alligator Trapping License valid through 11/1/2016): $62.00
So get busy folks. 1 down, 3 million to go... :-D