With the Scottish Premiership season starting on Friday, it was another strong test for Derek McInnes’ squad against the English outfit.
Rangers lined-up with Ivor Pandur in goal, behind a back four of captain Dujon Sterling, Ben Godfrey, Emmanuel Fernandez and Tuur Rommens.
Cammy Devlin made his first start for the club in midfield alongside Mohamed Diomande and Thelo Aasgaard, while Djeidi Gassama and Finlay Curtis supported striker Ryan Naderi.
It was a good start from Rangers, Cammy Devlin and Diomande combined in the middle of the pitch before a lovely turn from the latter opened up space for a strike, but his left footed effort was held by Mads Hermansen.
There was another opportunity from a set-piece as Thelo Aasgaard lifted a ball into the box, with Ben Godfrey rising to head toward goal but it was dealt with by the visiting number 1.
West Ham almost had an opening of their own as the half hour mark approached. Mohamadou Kante fed the ball forward into the path of Pablo who was looking to drive into the box and get a shot away, but Dujon Sterling blocked the opportunity with a good tackle.
There were four changes for Rangers at half-time as Dan Neil, Lawrence Shankland, Oliver Antman and Youssef Chermiti were introduced in place of Cammy Devlin, Djeidi Gassama, Findlay Curtis and Ryan Naderi.
Taty Castellanos had a shot over the bar early in the second half, before Mohamed Diomande saw a header blocked by Hermansen.
A set-piece opened another chance for Rangers after a foul on Thelo Aasgaard just outside the box. The Norwegian international stepped up to free-kick and forced a good save from the West Ham goalkeeper with a powerful hit.
Unfortunately for Aasgaard, it was his final action of the game as he appeared to suffer a shoulder injury in the build-up to the free-kick and was unable to continue with Tochi Chukwuani coming on in his place.
There was a great chance for Lawrence Shankland with just over 10 minutes remaining. A good delivery was swung into the box by Tuur Rommens and the striker guided a header towards goal, but Hermansen was down quickly to gather.
Jarrod Bowen almost got a break from a long goal kick from the other end, but Pandur was alert to the danger.
Attention now turns to Friday’s Scottish Premiership opener away to Dundee United.
RANGERS: Pandur, Sterling, Godfrey, Fernandez, Rommens, Devlin (Neil, 46), Diomande (Bajrami, 81), Aasgaard (Chukwuani, 64), Gassama (Antman, 46), Curtis (Chermiti, 46), Naderi (Shankland, 46).
Subs: Kelly, McCrorie, Nsiala, Hutton, Nsio, Barron, Cameron, McCausland, Miovski. West Ham: Hermansen, Walker-Peters (Mayers, 84), Kilman, Ward-Prowse (Earthy, 73), Castellanos (Orford, 73), Mavropanos (Casey, 84), Pablo (Golambeckis, 84), Bowen (Marshall, 84), Lamadrid (Potts, 73), Scarles (Cornet, 84), Kante (Ajala, 73).
Subs: Alphonse, Herrick.