It would be much easier if you can convert geotiff to tiles using GDAL (gdal2tiles utility), then to a mbtiles package, and then use offline tile viewer tool like Mapbox iOS SDK:
gdal2tiles.py -r cubic --s_srs EPSG:900913 mygeotiff.tif mytiles
mb-util --scheme=osm mytiles/ mytileset.mbtiles
If you really need to read geotiff directly, then I would use same GDAL library (libgdal) which is crossplatform and can be compiled to iOs. See stackoverflow articlestackoverflow article about it.