Yes, use a water stone.
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you must trade with gold or silver in order for poliwhirl to evolve. kings rock
use a water stone o evole it
In the water
There are 4 classic trade-evolution Pokemon that appear in almost all games. Those are Machoke, Graveler, Haunter and Kadabra. Also, all the Pokemon that uses the metal coat or the King's rock to evolve has to be traded while holding that item. So Slowpoke (If you want Slowking and not Slowbro), Poliwhirl (If you want Politoad and not Poliwrath), Onix and Scyther also need trading to evolve. There might be a couple from Gen 4 that need trading, but I'm not that familiar with those. Hope this helps :)
Rhydon cannot evolve in Pokemon Silver/Gold/Crystal.