The animal inspectors were called out following reports that an ostrich-like bird was in the residents’ car park of Princess Gate.
Four workers then were able to corner the rhea using a special hook.
They were then able to sit on the bird to prevent it flapping its wing or legs and injuring itself or the officers.
The rhea was then put into a cage and driven away.
RSCPA inspector for West Yorkshire, Carol Neale, who was in attendance, said: “We don’t get these things every day, in 26 years I have never seen one.
“Health and safety was our main issue, with the beak and the talons, they are very strong and could do a lot of damage to us and to itself.
“With teamwork, we were able to get it done and the bird is absolutely fine.
“We’re now going to have to find out where it came from.”
Indigenous to South America, the rhea is a flightless bird and related to the ostrich and emu family.
It is likely to have escaped from a breeding farm.
Princess Gate resident, Dave Hardy, was the first to spot the bird, which had white feathers and stood over six-feet tall at full stretch, from the rear window of his property.
He spent more than two hours monitoring it as it paced up and down the fence line at the back of the properties looking to get into the field behind.
He said: “I was just making coffee and couldn’t believe it when I saw it, I had to shout my wife.
“I think anybody would be shocked.
“We have no idea where it came from - if it was a lamb, you’d think it came from the next field, but not this.
“It’s only 50 metres from the motorway it if it had got over that fence it would have caused mayhem, but I was really impressed by the way the RSPCA handled things.”