"In hot weather the adult birds often can't keep the chicks cool in the nest so they pick out one or two of the smallest and chuck them out."
The four-week-old chick, which has not been named, will be looked after at the centre for up to another five weeks.
During that time she will learn how to hunt insects and fly.
Over the past two summers the centre has successfully reared 24 chicks who have been given the heave-ho from home and released them back into the wild.
"We handle them so they calm down and there's no stress on the birds," Mr Webb said.
"When we transfer them to an outside aviary we don't engage with them and they learn how to hunt insects."
Mr Roberts advised people not to try and rear abandoned moreporks themselves because they required a special diet with the correct vitamins.
"Otherwise they can develop deformities," Mr Webb said.