The honest answer would be, nobody knows yet. The
current knowledge is that the electron seems to be
a 'point particle' and has refused to show any signs
of internal structure in all measurements. We have
an upper limit on the radius of the electron, set by
experiment, but that's about it. By our current
knowledge, it is an elementary particle with no
internal structure, and thus no 'size'.
Answered by: Yasar Safkan, Ph.D. M.I.T., Software Engineer, Istanbul, Turkey

'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'