The character has 口 (mouth) on the left - a bird's beak is its mouth for pecking. The most common compound is 啄木鸟 (woodpecker - literally 'peck-wood-bird').
Mouth radical on the left - the indexing radical. For a bird the mouth IS the beak, so 口 supplies the action: striking, pecking, taking food. Sits in the same mouth-action family as 吃 (eat), 咬 (bite), 吞 (swallow).
phonetic
豖chù
shackled pig
Right side 豖, a variant of 豕 'pig' with an extra stroke marking a tied leg, supplies the sound (chù to zhuó with tone and onset drift). It contributes a faint scratch-and-root image too: just as a pig roots in dirt, a bird pecks at the ground.
