I want to join 5' end to 3' end of ssDNA. OR if using reverse complement of it and then attaching to to original ssDNA can I make them join? Something like the picture I have attached.
Have you tried CircLigase™ ssDNA Ligase from Epicentre? It should not require any oligo. However, it seems that your idea should work also. The complementary and spanning oligonucleotide may be quite short, I would say ~15 bases on either side to provide a platform for a conventional DNA ligase.
I have funny idea. If you have complimentary strand shorter by few nucleotides, and than form the circle like in your picture. You should be able to ligate only strand you want to circularize, and than degrade complimentary one by some exonuclease. It might be more difficult than the direct ligation, but the yields should be really high. Hope it make sense.