Is it possible to use a credit card when taking a taxi from the airport to hotel?
YES. All the taxis take cards now.
FROM THE AIRPORT
Go out the doors from the Arrival Hall to the Sidewalk and look to your left to see the FoTaxi Kiosk. Go to the window and tell the person working where you want to go. If it is a street address like for an AirBnb be sure to tell them what District. Why? Street names are sometimes repeated in different Districts.
You will be given a slip of paper with your destination on it and the taxi number.
Walk a few feet to the curb and your taxi will pull up.
In 30 to 40 minutes, tops, you will be in Budapest. Charges will be under 12.000 ft.
IN TOWN
Once in town if you need a taxi be sure to book it yourself. Never let a hotel do it unless you have mucho $$$
Never hail a taxi and never get one from a taxi stand. This is more about cost and good practice than anything else. The days of taxi crooks are pretty much over, but still, its good practice and cheaper.
I like City Taxi and they have a useful phone app for ordering the taxi.
RETURN TO AIRPORT
You can use City or FoTaxi to return to the airport if you want, but any company can drop off at the airport.