map.setMapType(GoogleMap.MAP_TYPE_NONE);
String mapId = "<Your Map ID>";
String accessToken = "<Your API access token>";
TileOverlayOptions mapBoxTileOverlayOptions = new TileOverlayOptions();
mapBoxTileOverlayOptions.tileProvider(new MapBoxTileProvider(mapId, accessToken));
map.addTileOverlay(mapBoxTileOverlayOptions);
References: