The term Runic Alphabet can refer to any of several closely-related real-life historical writing systems. Multiple games in the Fire Emblem series contain references to real-world runes.
The earliest known instance is in Fire Emblem: The Sacred Stones, where symbols from the Elder Futhark alphabet appear in the menu background. The largest line can be assumed to read "FIRE EMBLEM." The text above is mirrored and starts with "FIRE EMBLEM" and ends with the same unknown word as the one at the bottom of the screen. The rest appears to be nonsense.
In Fire Emblem: Path of Radiance and Fire Emblem: Radiant Dawn, the two races in the game are named after runes, Laguz after the Elder Futhark rune meaning "lake" and Beorc after the Anglo-Saxon rune meaning "birch," a descendant of the Elder Futhark rune Berkanan. In the Japanese version, the ancient Zunanma civilization is named Mannaz after the Elder Futhark rune meaning "man."
Fire Emblem Awakening has letters that resemble runes, but they have no relation to any real-life runic alphabet. The writing on the Falchion and Fire Emblem is an original alphabet, and the text visible when casting some magic in battle is the Ancient Language font from Path of Radiance and Radiant Dawn.