What is my birth rune?
The tables that hand out a rune by birthday divide the calendar by the futhark row, and different books draw the lines in different places. No source has a birth rune: the row is the order of an alphabet, not of a year. The tables themselves are modern.
Where this comes from
no source no text before the twentieth century ties a rune to a birthday
The half-month tables that assign each person a rune by birth date belong to the modern rune books. Nothing older carries them: not the poems, not the inscriptions, not Tacitus. The row itself is attested as an alphabet: the Kylver stone in Gotland lists all twenty-four runes in order. An alphabet has no birthdays.
What the poems say
The poems go through the letters in the futhark order, one stanza each. No stanza mentions a month, a season of birth, or a person the rune belongs to. What they do say about each rune is here.