Is there a chart of all possible Chinese syllables using Hanzi?
我 should be 哦, in the -o group: o, bo, po, mo, fo, lo. It is conflated with the -uo group: wo, duo, tuo, nuo, luo, guo, kuo, huo, zhuo, chuo, shuo, ruo, zuo, cuo, suo.

The -i group is also missing: zhi, chi, shi, ri, zi, ci, si (different from yi, bi, pi etc.). Back to the drawing table. And don't neglect the tones.

Has it been done before? Yes:


  
  (source)


and


  
  (source)


and  etc.