What you are looking for is eth_getCode
:
Returns code at a given address.
Example:
$ curl -X POST -H "Content-Type: application/json" --data '{"jsonrpc":"2.0","method":"eth_getCode","params":["0x0289eC8BDFBF5f6d90102E752e674F18f7a8Ed03", "latest"],"id":1}' http://127.0.0.1:8545
{"jsonrpc":"2.0","id":1,"result":"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"}
Example with Geth:
> eth.getCode("0x0289eC8BDFBF5f6d90102E752e674F18f7a8Ed03")
"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"
https://rinkeby.etherscan.io/address/0x0289eC8BDFBF5f6d90102E752e674F18f7a8Ed03#contracts