Is there a test for systemic lupus?  

Not really. The diagnosis is made based on symptoms, physical exam findings and some blood work. People frequently refer to some of the antibodies checked in lupus as "lupus tests" but just because the test is positive does not mean you have lupus. Less than 1/2 the patients i see for a "positive lupus test" end up having lupus.
Yes, blood tests. There are several blood tests to look for and to confirm a diagnosis of lupus, in a person with some symptoms of lupus (sle).