The Fostering Network said 7,180 new carers are needed to replace those who leave and to increase the pool of carers to be able to provide suitable homes for the diverse range of children coming into care.
It said shortages are most acute for older children and sibling groups, with almost all fostering services it surveyed (97 per cent) in need of carers for teenagers, while 86 per cent are calling for more carers for sibling groups.
"Without more foster carers for teenagers, young people have to be placed with foster carers who live far from their families, friends and schools and are being split up from their siblings," the charity said.
"Other teenagers are being placed with foster carers who, despite being excellent carers, are outside of their comfort zone when it comes to caring for teenagers or may not have the specific skills or experience to meet the needs of a particular teenager.
"All this means that the stability of foster carer placements for teenagers is being undermined, which in turn affects their educational and other outcomes."
The charity has launched the appeal to mark the start of Foster Care Fortnight which begins today.
The charity said there are currently 455 sibling groups that have been separated, despite being assessed as being able to live with each other, while six out of 10 looked-after children are teenagers, said the charity.
It added: "Our relationships with our brothers and sisters are often some of the most important and longest lasting of our lives. Yet children in care, already dealing with the trauma of being separated from their parents, are all too often split up from their siblings as well.
"Sometimes brothers and sisters will be separated because it is in their best interests, but in general finding a foster family that can keep siblings together is crucial."
There is also a shortage of parent and child foster carers, who offer parenting support to young mothers or fathers who are having difficulty looking after their babies. More than half (56 per cent) of fostering services said they are in need of more of them.
The figures show that 5,900 more carers are needed in England, 640 in Scotland, 440 in Wales and 200 in Northern Ireland.
The English region with the biggest shortfall is the North West, where fostering services need 1,050 more carers, with the lowest demand in the North East, where an extra 360 are required.
The shortage of foster carers is less acute than last year when the Fostering Network estimated that 9,070 more carers were needed. The charity said the lower figure this year is due to fewer foster carers leaving the role and a slowdown in recent increases in the number of children coming into care.