Oriented　object　detection　(OOD)　in　remote　sensing　images　(RSIs)　is　of　increasing　interest.　Since　RSIs　often　contain　many　oriented　objects,　it　is　valuable　and　challenging　to　discover　geometric　invariance　of　geospatial　objects　to　improve　the　model＇s　perception　of　rotation　angle　and　scale.　In　this　paper,　we　propose　a　twin-tower　detector　(T(2)Det)　for　OOD　in　RSIs.　Specifically,　T(2)Det　overcomes　the　challenges　posed　by　the　angles　and　scales　of　oriented　object　by　developing　a　self-supervised　(SS)　branch　that　exploits　geometric　invariance　based　on　the　main　branch.　Then,　we　design　a　twin-tower　(T-2)　loss　function　to　enhance　the　network＇s　ability　to　perceive　the　geometric　invariance　of　geospatial　object,　where　a　coarse　loss　function　and　a　fine　loss　function　are　introduced　for　both　branches　to　optimize　the　model　from　coarse　to　fine.　In　addition,　T-2　loss　function　optimization　strategy　based　on　global　or　refinement　modes　is　developed　to　achieve　the　trade-off　between　the　main　branch　and　the　SS　branch.　On　three　benchmark　datasets,　including　VEDAI,　HRSC2016,　and　NUAA-SIRST,　our　T(2)Det　achieves　competitive　performance　of　85.15%,　90.66%　mAP,　and　99.28　P-d,　respectively,　without　unnecessary　extra　features.