I am not aware of a built in way to do this, but there are utilities that others have written that can be plugged in to an ILE program on the i. Although these are RPG examples, I suspect you could do something similar with ILE COBOL.
Here is a good presentation about web services from Scott Klement, whom you may have heard of before.
Here is where you can get the code:
Here’s a utility from a well known technical writer, Bob Cozzi.
Also, these utilities look to have written before the new operation codes XML-INTO and XML-SAX were introduced in V5R4 of the operating system. Again, these are for RPG, so I don’t know if ILE COBOL has anything similar. But if not, you could always have your COBOL code call the RPG program to consume the web service.