There is (almost) no way to get the ABI if you only have the transaction hash and/or contract address.
I said almost because it is possible to reverse-engineer the contract. At least in theory. Reverse-engineering is always a difficult process and it might not work. There are some tools which attempt to do it for you but I don't really know how accurate they are.
Some more info on reverse-engineering: Is there a way to extract ABI from a deployed contract? (https://ethereum.stackexchange.com/questions/37931/is-there-a-way-to-extract-abi-from-a-deployed-contract)
Just to clarify some confusion in an another answer's comments: verifying your code on Etherscan isn't really a Ethereum term. It's only functionality which was (possibly) invented by Etherscan team. It's a handy feature but it's not necessary in any way. You can publish your code in the blockchain without providing the source code to anyone.