To determine the hybridization of a carbon atom, we need to count the number of atoms bonded to it and the number of lone pairs it has. In C2H2, each carbon atom is bonded to two other atoms (one carbon and one hydrogen) and has no lone pairs. This gives each carbon atom a total of two electron pairs to hybridize.

When a carbon atom has two electron pairs to hybridize, it undergoes sp hybridization. In sp hybridization, one s orbital and one p orbital combine to form two equivalent sp hybrid orbitals. These sp hybrid orbitals have a linear shape and are oriented at an angle of 180 degrees from each other.

Therefore, the C-hybridization of C2H2 is sp.