The short answer is no, not if the creative team did their research, which we have to assume they did. The long answer requires a little more exposition, so let’s break it down. Sauron adopted the Great Eye sigil during the Third Age (the era in which Tolkien’s most famous story takes place). “The Lord of the Rings: The Rings of Power” takes place during the Second Age, several thousand years prior. Immediately, that negates any chance of these two sigils being the exact same thing — again, provided that Amazon did their due diligence. Also, the Eye of Sauron doubled in meaning with the Palantíri (the ominous crystal balls seen in the first trilogy of films) that Sauron uses to usurp Sarumon (Christopher Lee). These have yet to be introduced in the Amazon series. So, if it’s not the Great Eye, then what is it?
Okay, so this is entirely speculation but it’s possible that Amazon recalled how integral symbols are to the mythology “The Lord of the Rings” trilogy. Middle-earth is a land of symbols, so it would make sense that the creative team behind “Rings of Power” opted to create a new sigil for Sauron to display that might call to mind some of the images that would later become associated with the latter-day dark lord.
For this to make sense, it’s important to understand a few things. First, that Morgoth is Tolkien’s version of the devil himself, fallen grace. Second, that Sauron is one of his many servants. Third, whenever Morgoth falters on his quest to conquer Arda (the world in which Midde-earth is but a continent), something that occurs with hilarious frequency, Sauron tries to strike out on his own. It is possible that this sigil is a physical representation of Sauron’s latest solo venture — a brand insignia of sorts.