Q: Can a rejected paper be revised and submitted to the same journal as a new submission?

If your paper has been completely rewritten and has a substantial amount of new data and interpretations, you can definitely check with the journal if they would consider it as a new submission. 

However, rather than submitting your manuscript directly and waiting for the journal's response, I suggest that you send a pre-submission inquiry. Mention that your paper had been rejected earlier, but that you have revised it considerably post rejection, and inqure if the journal would now be interested in it. You will have to explain in detail how the paper has been changed, how much of new data has been added, whether you have any new findings or interpretations. Additionally, you should provide the submission details of the previous manuscript for reference. 

If the journal editor feels that the revised paper may be of interest to his journal, (s)he will definitely reply to your e-mail. If (s)he gives a positive reply, you can submit the manuscript as a new submission. If (s)he feels that the paper would not be suitable for the journal, you can send it to a different journal. In some cases, the editor might also suggest a few journals that he feels might be a good match for your paper. For further help in selecting a target journal, you can watch this video for expert advice in this matter: Selecting a suitable journal for your manuscript.

You might also be interested in reading Tips for authors submitting a revised manuscript.