ENVI's ROTATE_DOIT will not handle an arbitrary rotation value, so to rotate the image using a different rotation value you would need to use IDL's ROT function.  You can get the rotation value from the file using ENVI's routine ENVI_GET_MAP_INFO which returns the map info structure that contains the rotation of the file.  You could pass this rotation value to your program that calls IDL's ROT function.  This may also require the use of ENVI's tiling routines if your files are large.