If the data is always in the format {^yyyy/MM/dd}
then you could use:
CONVERT(date,REPLACE(SUBSTRING(YourDateColumn,3,10),'/',''))
Ideally, however, you should be fixing your column to be the correct datatype:
CREATE TABLE Test (DateColumn varchar(13));
INSERT INTO Test VALUES ('{^2013/05/29}');
GO
SELECT *
FROM Test;
UPDATE Test
SET DateColumn = CONVERT(date,REPLACE(SUBSTRING(DateColumn,3,10),'/',''));
SELECT *
FROM Test;
ALTER TABLE test ALTER COLUMN DateColumn date;
SELECT *
FROM Test;
GO
DROP TABLE Test;