He appears in the mission "Loose Ends" as part of Sniper Team One, wearing a ghillie suit and providing overwatch for the strike team (Roach and Ghost). He and his partner Toad provide very critical help during the take down and defense of Vladimir Makarov's safe house, providing sniper support and taking out two armored trucks that were escaping from Makarov's safe house with Javelin missiles.
Archer and Toad are invisible once the player breaches one room in the safe house. They provide fire support, but cannot be seen if the player returns.
Archer and Toad can be killed by the player at the beginning of the level. If the player plants and shoots a claymore causing the explosion to kill them then they will not be penalized for friendly fire. The level will still proceed normally even including the scripted dialogue from Archer.