It is possible and even trivial but I am not aware of any application to do that task specifically.

There reason why the file size changes when rotated is that TIFF files are encoded losslessly as one would compress a stream of pixels components from one corner of the image to the opposite one. If you consider Run-Length-Encoding (RLE) which a common TIFF encoding, it is easy to understand why the same image will not compress to the same size after being rotated. It is equally likely that the file increases in size than it would decrease.

There is an easy way to get around that though and that is simply to change the tag which says which way pixels are ordered in the image. By simply changing the tag from a row-oriented ordering to the equivalent column-oriented one, the image is effectively rotated without any change to pixel data. You can read the details about the TIFF format here, just search for tag 274 (Orientation).

Honestly I thought no one used column oriented storage pixels so when I initially wrote a TIFF codec, I ignored that possibility for simplicity. As it would happen, one day we received such a TIFF image and my code did crash! Hopefully not many other developers took that short-cut either. It turns out that the file in question came from a scanner which did the scanning and encoding always exactly in the same way but set the orientation flag depending if it was fed a film-strip with frames in landscape or portrait orientation.