The round-robin tournament is a widely used format. One of its main advantages is that it allows players to compete against each other, reducing the impact of luck and providing a complete ranking for players. The round-robin ranking problem is to determine a ranking that is considered optimal or widely accepted among the players based on the tournament results. The Elo rating system uses numerical values to represent the relative skill level of players, providing a method for evaluating their strengths. This rating system, which is commonly used in chess tournaments, updates the ratings of two players based on differences in their ratings and the outcome of the match. In this thesis, we try to utilize the Elo rating system for ranking round-robin tournaments and resolving some of the challenges posed by the original methods. In addition, we provide conjectures based on our observations and ongoing research.