If you try to enchant shears using "/enchant @p silk_touch", it won't work and the game will say "Shears cannot support that enchantment". I'm pretty sure this is not intended as you can apply silk touch on shears through the use of Anvils.
EDIT: It seems this is not the case, and this simply happened because I was on Creative mode. Thanks to CreeperMagnet_ for pointing it out.
Nope. You can't apply silk touch to shears.