I just found the way, you just need to give null as parameter instead of an Exception, for example:
ACRA.getErrorReporter().putCustomData("myKey", "myValue");
ACRA.getErrorReporter().handleException(null);
These 2 lines will report this error:
java.lang.Exception: Report requested by developer
With the following as custom data in the report:
{myKey:myValue}