Garcia is much travelled having played football in Russia, Italy and Uruguay prior to joining the West Yorkshire outfit.
The stopper will make his Leeds bow in the behind-closed-doors match with Middlesbrough on Tuesday.
Grayson will be hoping Garcia impresses as much as one of the club's ex-Argentina trialists Luciano Becchio.
Becchio joined Leeds on trial and went on to sign a three-year contract and become a first-team regular alongside Jermaine Beckford.
"Walter is a player we've been made aware of," Grayson told the club's official website. "He's been training with us and will play against Boro."
Central defender Rui Marques is also scheduled to appear in what will be his first taste of competitive action since August.
Marques, who has made only six first-team appearances this season, has been sidelined with an Achilles injury.
Leeds Evens, Draw 12/5, Brighton 11/4