Can I drive in the United States with a Sri Lankan driver's license?

All states in the US have their own rules regarding foreign drivers. If you are a resident in any state then you need that state's driving licenses. The rules to determine if you are a resident can be obtained from the respective state's DMV. Since you are on a short visit, I will assume you do not fulfill the resident criteria.

Talking specifically about District of Columbia (DC), USA

Non-US citizens on visitor visas are not eligible to obtain driver licenses in the District of Columbia. source

If you are a visitor, you cannot apply for a DC drivers license. Period. However, in order to drive, you will need a valid driver's license issued by your home country and it should be in English. If it is not in English you can have it translated by your local embassy on an official embassy letterhead OR from a translation company.

If your valid, non-US driver license is not in English, you must attach an English translation from your embassy or from a translation company. The embassy translation must be on official embassy letterhead. The date of the translation must be on or after the actual date of the non-English language driver license. Translations from companies must be certified with a translation stamp, or notarized by preparing a notarized affidavit confirming the translation was prepared by a qualified translator and that it is both accurate and complete. source

Some states require an IDP (international driving permit) along with your valid license. However, the DC DMV does not mention any IDP requirements. If you will drive over into another state e.g. Virginia, Maryland etc (which are really close by) you should check their DMV information. But it never hurts to have an IDP as an extra precaution, after all, it's not your own country.

Foreign Nationals Driving in the United States

People who drive in the U.S. must have a valid driver's license. Some states require an International Driving Permit (IDP) from foreign nationals, in addition to a valid license from your own country. Contact the motor vehicle department of each state you will drive in for its requirements.

Short-Term Visitors If you intend on getting an IDP, you must do so in advance of your travel:

• The United States does not issue IDPs to foreign visitors. To get an IDP, contact the motor vehicle department of the country that issued your driver's license.
• If you want to rent a car, you may need both your license and an IDP. Find out the rental company's policies and other requirements in advance.

source

All of the links that I have quoted are official US government websites. A google search also leads to a website: www.washington.org; please note that this is a marketing organization for DC and not a US government website.

I would suggest contacting the DC DMV for any additional/official details:

Phone: (202) 737-4404

Email: dmv@dc.gov

Live Chat: https://dmv.dc.gov/page/dmv-live-chat

According to this guide, you will need to apply for an International Driver Permit before being able to drive in Washington, D.C. You can contact you local DMV for instructions on how to obtain an IDP.