The archer card has the following statement……… As an additional cost to rez Archer, the Corp must forfeit an Agenda. My question is can the Corp player forfeit the Agenda from his HQ, completed Agendas and those in Servers or is there a restriction?

Core rule book page 22:

"Forfeiting Agendas-

Some card abilities require the Corporation or Runner to forfeit an agenda. When a player forfeits an agenda, he selects any agenda in his score area and permanently removes it from the game (it does not go to Archives or the heap). He no longer scores points for the forfeited agenda."

d4rkwing said:

Scoring is good. Not scoring is not good.  Wait until you score the Agendas: Priority Requisition or Accelerated Beta Test to rez Archer and ignore that requirement.

Big Borg said:

As a backup plan with Weyland (where archer originates from) you could forfeit 'Hostile takeover'. It can be scored in one turn, has a nice effect and doesn't drain you of your BIG agenda scores (although it leaves you with bad publicity) but as archer is quite powerful it might be worth the pains, especially in early game.

 Thanks guys really appreciated.

I use Archer in my NBN deck. 

It's no big deal sacrificing a 1 point agenda for an awesome piece of ICE.