DCRA maintains records of all permits approved. On a weekly basis they post a list (in PDF) of permits issued that month-to-date and at the conclusion of the month will post the monthly list. If there is no link, the permit list has not yet been released.
To see permits (and other information for a single particular address) check out PIVS–Property Information Verification System. PIVS
DC has ceased publishing Building Permits Issued pages but you can still look up a permit by property address or legal description using PIVS. Districtre.com 9-01-13