If you were to change the question a little to ”who first theorized that Mars was a planet”, then an answer can be found. Nicolaus Copernicus is the first astronomer to postulate that Mars and a few other bodies known at the time were planets. The heliocentric theory that he published in 1543 marked the first time that astronomers widely considered the possibility that the Sun was the center of the Solar System instead of the Earth.
While no one knows who first discovered Mars, we do know who made many of the discoveries about the planet. It is known that Tycho Brahe, a Danish astronomer made accurate calculations of the position of Mars as early as 1576. Johannes Kepler theorized that the orbit of Mars was elliptical in contradiction to what astronomers believed at the time. He soon expanded that theory to encompass all planets. In 1659, Christian Huygens, a Dutch astronomer drew Mars with the observations he made using a telescope he designed himself. He also discovered a strange feature on the planet that became known as Syrtis Major.
On November 28, 1964, Mariner 4 was launched successfully on an eight-month voyage to the Red Planet. It made its first flyby on July 14, 1965, collecting the first close-up photographs of another planet. The pictures showed many impact craters, some of them touched with frost in the chill Martian evening. The Mariner 4 spacecraft was able to function for about three years in solar orbit, continuing long-term studies of the solar wind environment and making coordinated measurements with Mariner 5.
There are currently six spacecraft in orbit around Mars or on its surface and several more are in the planning or design stages. Five are gathering data at an amazing rate, the other(Phoenix) is non-functioning. New discoveries like subsurface water ice and methane plumes in the atmosphere are being made on a regular basis. Scientists may not be able to give an answer to ”when was Mars discovered”, but they can offer answers to thousands of other questions and the list is growing as we speak.
We have recorded an entire episode of Astronomy Cast about the planet Mars. Listen to it here, Episode 52: Mars.