Yes, as of 2019, you can use London Visitor Oyster Cards on the Heathrow Express, which travels direct (no stops) between Heathrow and Paddington station. This will cost you up to around £25***, depending on time of day. Alternatively, you can purchase your Heathrow Express e-ticket to/from Paddington Station from British T.I.P.S.
For a budget option, you can take the Underground’s Piccadilly line service. This goes into the city and stops at multiple stations on the way as it is a commuter train. Although this is a cheaper option (at around £6***), bear in mind that it does take longer (around 1hr by Tube vs 15 minutes by Heathrow Express) and the trains are usually more crowded.
***accurate at time of posting and subject to change.
