Is there a way with the Etherscan API you can get all the erc20 token balances for a specific address?
As explained here, you can see token balances with their web UI (the token tracker dropdown).
Does their API provide equivalent functionality?
As far as I can tell, you can only query for a specific token of which you already have the address. I need functionality equivalent to Ethplorer's API endpoint getAddressInfo/{address}.
Best Answer
As previously mentioned it doesn't appear possible using etherscan. But it's possible using the (free) ethexplorer.io API.
The format is:
http://api.ethplorer.io/getAddressInfo/[YOUR_ADDRESS]?apiKey=freekey
For example:
http://api.ethplorer.io/getAddressInfo/0x32Be343B94f860124dC4fEe278FDCBD38C102D88?apiKey=freekey
API documentation is here:
https://github.com/EverexIO/Ethplorer/wiki/Ethplorer-API
Website:
https://ethplorer.io