San Diego traded the first pick (michael vick) to atlanta in 2001
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NFL Draft
Vick was selected first in the 2001 NFL Draft by the Atlanta Falcons. The San Diego Chargers had the number one selection but traded the rights to the first overall choice to the Atlanta Falcons a day before the draft, for which they received the Falcons' first round pick (5th overall) and third round pick in 2001.[13] Vick was drafted in the 30th round of the 2000 MLB Draft by the Colorado Rockies, despite not playing baseball at Virginia Tech.
Also
Ernie Davis to Cleveland Browns from Washington Redskins in 1962
John Elway to Denver Broncos from Baltimore Colts in 1983
Eli Manning to NY Giants from San Diego in 2004