Wrexham boss Phil Parkinson said of Rodriguez: “He’s an experienced striker with real quality and we’re looking forward to working with him.”
Parkinson has been keen to strengthen his frontline as Wrexham, who are owned by Hollywood stars Ryan Reynolds and Rob McElhenney, bid for promotion to the Championship.
He described Smith, who has 11 goals this season, as “a fantastic addition to the squad”.
“Sam is a player we’ve been pursuing for a while,” Parkinson added. “He’s a striker who’s done really well over the last few seasons and he’s at a great age.”
Smith came through the Reading academy after he was released by Manchester United and made his senior debut for the Royals in August 2017.
He subsequently had loans spells with Bishop’s Stortford, Oxford United, Shrewsbury Town, Cambridge United, Tranmere Rovers and Cheltenham Town.
Smith left Reading at the end of his contract in the summer of 2021 and joined Cambridge on a permanent deal.
After two seasons at Cambridge he rejoined Reading in July 2023.
Smith scored 27 goals in 63 games during his second spell with Reading, including 11 this season.
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