Your best bet is regular street (metered) parking. That might be a challenge during regular business hours during the week but I was there last Friday for a Christmas concert and had no trouble finding plenty of available spots along I Street just a block away.

Unlike the other two who answered this question, yes, they do offer occasional concerts, especially around Christmastime. I attended one last Friday where a local professional choir and small orchestra presented Handel's Messiah. It was superb. How other reviewers say that "doesn't glorify God" is beyond me, especially when they cite people like Ariana Grande and Taylor Swift as some who do. Seriously? So anyway, the answer to your question is YES. Check the Cathedral's website. On there you'll find an events calendar where such concerts are listed.