As someone already mentioned, there is the Shulchan Arukh which says
Orach Chayim 8:4 - "One should place 2 fringes in front and two behind him in order that he should be surrounded with fringes."
But this is not regarded as a halacha. You can see this by the opening line of this same section.
Orach Chayim 8:2 -"The manner to wrap oneself goes according to the way people wrap themselves in clothing."
These are suggestions, not halachically binding. You find other codifications making similar mentions or suggestions.
Such as Nehar Misrayim, written in the 1900s on the laws of Egyptian Jewry. i actually have pictures to verify this was how it was done. So you have instances of an entire community, post Shulchan Arukh, not following what was written. Why? Probably because they already had a custom and did not feel the need to follow a new suggestion.
Nehar Misrayim Halachoth Sithsith 4:"
ד) במצרים רובא דרובא דהמוני עם משלשלין כל הארבעה ציציות לצד פניהם והטלית מקופל על צוארם וראוי להודיעם שלפחות בשערת העטיפה. יברך ויתעטף בו ראשו ורובו ויעמוד כן כדי הילוך ארבע אמות ואח״כ ישלשלנו על כתפו."
"4) In Egypt the most common way is that one drapes all four ṣiṣioth to their front and the tallit is folded on their neck. And it's appropriate to inform them in their time of wrapping. He blesses and wraps his head and most of his body in it and will stand up in the space of four cubits and afterward will drape it over his shoulder."
You may say that this custom could be a recent development, or a deviation away from the Shulchan Arukh. But the Yemenite custom is to also drape over the neck and shoulders with all four sisioth in front, and this custom very likely to predates the Shulchan Arukh.
As for written sources that predate the Shulchan Arukh, Rav Sa'adyah Gaon and the Radbaz both say that one should wear a tallith with it draped over the neck and then both sides thrown back over ones shoulder so that all sithsith are on ones back, in order to fulfill the words of a midrash. These are some of the earliest, and in the case of Sa'adyah Gaon, most authoritative opinions one can rely. If you would like to see or hear the specific sources, you can watch a video by Rabbi David Bar Hayim here
So in short. No, there is no way to wear a tallith according to halacha. It's a custom, and a matter of preference, with many differently valid suggestions on how it should be done. In the end you will probably be ostracized for doing anything contrary to the status quo of the community, so a more pertinent question may be, is one allowed to wear a tallith any way he pleases even if it's against the community norm?