There are many tools you can use for automating your API testing. Those are free and open source as well.
I mostly use SOAP UI, JMeter and Axis 2 framework for test automation of API.
SoapUI is one of the most widely used open source API testing tool for SOAP and REST APIs. SoapUI offers SOAP Web Services functional testing, REST API functional testing, WSDL coverage, message assertion testing and test refactoring.
The Apache JMeter™ application is open source software, a 100% pure Java application designed to load test functional behavior and measure performance. It was originally designed for testing Web Applications but has since expanded to other test functions.
Axis 2 framework https://axis.apache.org/axis2/java/core/
Apache Axis2™ is a Web Services / SOAP / WSDL engine, the successor to the widely used Apache Axis SOAP stack. There are two implementations of the Apache Axis2 Web services engine - Apache Axis2/Java and Apache Axis2/C
I use SoapUI if I have to just automate API functinality testing. I use Axis 2 if I happen to integrate API functionality testing with existing test suite. And I use JMeter if I am using REST API.
Hope that helps!