Is it possible to make burger buns pans made with paper tape?
If by "paper tape" you mean "strips of (food safe) paper or parchment" then yes, it's possible.

But before we talk about the how, let's have a quick look at the why first:
Most cooks want to match the size of the bun to the size of the patty or vice versa. Unfortunately, some recipes can be a bit unpredictable as far as the rising and expansion of the buns are concerned, and so are the abilities of the various bakers when it comes to proper shaping. A burger bun pan limits the sideways expansion, thus determining a maximum diameter. And if the bun can't expand sideways, it will go up.

Now, how you achieve that is up to you.
The aforementioned hamburger bun pans (aka mini pie pans, btw.) are but one solution. Others are baking rings, the tops of canning jars, strips of tinfoil, strips of parchment, a parchment collar inside a tin, parchment around a tin. (The latter two are probably overkill for your case.)

In short, for tinfoil or parchment you take a strip that's an inch or two longer than your desired diameter and a few times as wide as your desired height. You fold it lengthwise a few times for increased stability, then secure the overlapping ends - a stapler comes to mind. Tape will probably not stick to parchment (depends on the brand) and is not supposed to go in the hot oven. In a pinch, a piece of string (cotton, not plastic!) can work as well. The tinfoil link above has also step-by step instructions.

I personally use neither - I shape my buns until the surface is taut and usually they turn out nice enough. So in addition to crafting rings, you should also read up on how to properly shape buns.