That would be difficult, as Tetris wasn't invented until 1984 and Mendeleev published the first Periodic Table in 1869.

However, the Tetris game is based on certain ancient principles. Its inventor, Alexey Pajitnov, is a Russian computer engineer, working in computing research and development in what was then the Soviet Union. The name Tetris is based on the Greek word for four (tetra) and the game of tennis. The tennis part is partly because Pajitnov likes playing tennis, but the tetra part is because of the game's structure. The pieces in the game are based on the polyomino, a geometric figure made up of joined squares (ie, with four sides) of equal size. Puzzles based on this figure go back to ancient times.

As you can see here, the Periodic Table is structured in a similar way. That's the nearest thing to a connection I can see - but you could try asking a science teacher about this.