Can I get a VOA at Shenzhen traveling with an us passport?

As a US citizen, you are eligible for Shenzhen VOA. By the way, you should be informed that the price for this particular visa for US citizens is 956 CNY. You can pay for this fee with several credit cards, but also in cash that you can obtain at one of many Hong Kong money changers. The only currency accepted is mainland Chinese currency.

I’m making a connection in Frankfurt then Shenzhen, can I get the VOA in Shenzhen airport? The same day?

Wait, you will depart from Shenzhen to some other country during the same day, right?

In that case, you don't need any kind of visa because you are covered by 24 hour visa free transit scheme. In other words, if your flight to Shenzhen is a direct (nonstop) one from Frankfurt and your flight out of Shenzhen is of the same nature (direct, nonstop), then you are eligible for 24 hour visa free transit in Shenzhen.

Could you confirm that? I would like to give you a reliable information, so could you supply with your entire itinerary, please?

If you are making a connection in Shenzhen and depart from the city during 24 hour time frame, then you don't need any kind of visa because you will be covered by 24 hour visa free transit. Your flights to and from Shenzhen have to be direct (nonstop) and without any additional landings within mainland China. For example something like this:

Frankfurt - Shenzhen - X country (different than both Germany and mainland China)

Could you just supply with your entire itinerary and we will be able to give you a precise answer on this subject. I assume that you will not need a visa on arrival, but I can tell that only after you supply with your itinerary.