Dicamba is used as a pre- and postemergent herbicide for broadleaf weeds. The residues of dicamba disappear within several weeks or months, depending upon the weather. It is relatively mobile in the soil. We recommend that you do not plant vegetables or other edible crops in that garden site this year.
Our Extension turfgrass specialist thinks the dicamba will have broken down by next year, so you should be able to plant then. You might try a green manure crop to keep weeds down this year. This would also help determine when/if enough herbicide has deteriorated to enable you to plant. If the green manure crop grows, other plants should as well.