Phi is, above all things, the 21st letter in the Greek alphabet, so it's hard to say who created it. However, the number commonly attached to it, the golden ratio, has a long history, starting with the mathematicians of Ancient Greece, and has been studied, used, and approximated ever since. Just a few of the mathematicians who studied Phi are Euclid, who gave the earliest known definition of the golden ratio; Kepler, who described it as one of the two greatest feats of mathematics (along with the Pythagorean Theorem); Michael Maestin, who was among the first to give a rough approximation of the golden ratio's value; and Mark Barr, who first used the letter Phi to describe the ratio.
So, I guess in the end the creation of Phi was sort of a group effort.
Delta Phi was created on 1827-11-17.
Phi Sigma Sigma was created on 1913-11-26.
Phi Zeta was created in 1925.
Tau Phi Sigma was created on 1992-11-11.
Omega Phi Chi was created on 1988-11-09.
Phi Gamma Delta was created on 1848-05-01.
Eta Sigma Phi was created in 1924.
Alpha Sigma Phi was created on 1845-12-06.
Kappa Delta Phi was created on 1900-04-14.
Mu Alpha Phi was created on 1927-10-24.
Sigma Pi Phi was created in 1904.
Phi Delta Theta was created on 1848-12-26.