We don't know for sure.
The word "calcar," found in homer, may in some contexts refer to spurs. We have also found Roman spurs in northern Europe. A fourth century vase shows an Amazon warrior wearing a spur, but only on one leg.
Roman spurs were straight or claw shaped and quite sharp - some of them even had a guard to keep them from penetrating the horse's skin too far. (Modern horsemen consider making a horse bleed with the spur to be abuse). These guards may eventually have evolved into rowels - which first appeared in 10th century Spain. Early spurs were apparently secured to a rider's boot or sandal with buttons rather than with straps around the foot as are used today.