Yes, take a look on class - http://lucene.apache.org/solr/4_7_0/solr-test-framework/org/apache/solr/SolrTestCaseJ4.html
All you need is to extend this class, and in test method you could access Solr, send queries, assert response, etc.
Just an example of this kind of test from Solr repo - https://github.com/apache/lucene-solr/blob/c3ef419e4fb720866e88e0020b182de3e25a4fbb/solr/core/src/test/org/apache/solr/search/TestFieldSortValues.java