You can do rolling circle amplification.

I agree do circle amplification and after that if you gel electrophoresis you can say by the band it is circular or not.

The easiest way to test for circular DNA is agarose gel electrophoresis: covalently closed DNA is supercoiled and moves differently from nicked or linear DNA. So you should very carefully isolate DNA to keep it covalently closed (careful pipetting!!). Then take part of it and run it through a needle to break it (partially) or do a very short DNAse treatment (as for Klenow reactions) at low concentration of DNase and run both samples on a gel. In the second sample you should ideally see three bands (closed circular, nicked circular, linear) in the other you should not see more than two bands (closed circular, nicked circular) dependent on the quality of your originally isolated DNA. You may make a series of DNase digest in order to find the right treatment.

Thank you all for joining my question but in my question, I meant "How did circular DNA be demonstrated the first time in history?".

Sorry for my deficiency!

by electrophoresis : after a simple single digestion, only one band appear.

Sorry for my misunderstanding. Circular genomes were first established by genetics, but the first physical demonstration was to my knowledge b y electron microscopy of bacteriophages with circular genomes or plasmids (Kleinschnidt technique of DNA spreading: Kleinschmidt et al. 1962, BBA 61:857). Molecular demonstration by electrophoresis came later.

Now I know what to write in my report! Thank you all so much!