On 13 January 2010, Rodríguez completed a free transfer to Liverpool, signing a three-and-a-half-year deal. After securing his signature, Rafael Benítez described him as "comfortable on the ball, can pass and keep possession. He is good at getting into the box and scoring goals and a good finisher", and the player was given the number 17 shirt, making his debut for the club as a second-half substitute in a Premier League match against Stoke City on the 16th; his first full start came a week and a half later, in a 0–0 away draw to Wolverhampton Wanderers.
In his first games for Liverpool, Rodríguez picked up two league assists, both of which were for former Atlético teammate Torres. He scored his first competitive goal in a 4–0 win over Burnley at Turf Moor on 25 April 2010, playing the full 90 minutes.
Rodríguez scored in Diego Maradona's first game in charge of Argentina, a 0–1 friendly win in Scotland. On 19 May 2010 he was named in the squad of 23 for the 2010 World Cup in South Africa and, in the last home game before the finals five days later, scored twice against Canada, netting from a freekick from a sharp angle and after receiving a pass from Carlos Tevez in an eventual 5–0 win.