Shannon Murray arrived at the city's central station on Tuesday night and said the driver of a saloon vehicle "started yelling at me" and told her to use a larger taxi instead.
Ms Murray said she was "humiliated" and praised others who refused to get in the cab because of how she was treated.
Cardiff council said no complaint had been made.
Ms Murray - who was left paralysed from the waist down after a diving accident when she was 14 - has campaigned for better representation of disabled people in the media for 20 years and appeared in a number of dramas, including BBC One's Casualty.
On Twitter, she said: "I moved towards the car opened the front door at which point the driver started yelling at me, shouting that I couldn't get in his taxi I had to use a wheelchair taxi.
"I asked why and he just kept pointing at my chair shouting it wouldn't fit."
She said she prefers using saloon taxis as she can sit on a seat rather than her wheelchair.
Despite the "embarrassment and the humiliation", she said she stood her ground and told the driver her wheelchair folded up perfectly to go in the boot.
Ms Murray said she asked for his licence number and would report him, before another taxi gave her a ride.
She praised other people who did not get in the first driver's car: "One by one every single person in the queue refused to get in his cab because of the way he treated me.
"I don't know any of their names, but to the seven or eight people who had my back I thank you, from the bottom of my heart, thank you."
A spokesman for Cardiff council said it was an offence to refuse a fare that starts and ends in the city's boundaries without reasonable excuse.
"We ask everyone who wants to make a complaint against a driver and is willing to give their evidence to committee, to contact us so we can take action," he added.
An actress has said she was refused a taxi ride in Cardiff because she was in a wheelchair.