Looking on the internet deeply has found these results:

I will do that. is the most popular phrase on the web.

I will do so. 128,900,000 results on the web	I will do that. 117,100,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
to try and make this move faster, and I will do so. Having said this, if forty Members now stand up and make a request for the quorum to be established, I will do so. I was not expecting to speak but, as you have asked me, I will do so. There is no problem, I will do so. Nay, I will do so. I have sworn to put this man away, with any and all legal means at my disposal, and I will do so. You can challenge me and you should as often as you like	Then I will do that. I will do that. If it is I have to go to court personally, I will do that. Okay, thank you, and I will do that. You discharge these. I will do that. And I promise you I will do that. Okay, yes, I will do that. And I will do that.

I will do so.

128,900,000 results on the web

I will do that.

117,100,000,000 results on the web

More popular!

to try and make this move faster, and I will do so.
Having said this, if forty Members now stand up and make a request for the quorum to be established, I will do so.
I was not expecting to speak but, as you have asked me, I will do so.
There is no problem, I will do so.
Nay, I will do so.
I have sworn to put this man away, with any and all legal means at my disposal, and I will do so.
You can challenge me
and you should as often as you like