Let me assure you, your car is actually a quite capable machine. It was likely designed by smart people, and tested extensively before going to market. Moreover, the paved road you're on and currently favorable weather conditions are both quite conducive to driving.
In short, there's very little reason, person-in-front-of-me, that your simple right hand turn would necessitate slowing down to a near stop, swinging out into the left lane, and hooking back as though you were squeezing a firetruck into a one-car garage.
Trust me, the turning radius of your Civic can handle getting into the Kroger parking lot. I'm quite confident on this point. Just turn the wheel, you'll be fine.
All though I would like to ask something. If you're taking all that trouble to make the turn, why not use your turn signal too? If you misjudged the angle of attack, at worst you'd wind up with a little scrape on your bumper. But the signal drastically reduces the likely hood that someone won't anticipate your sudden deceleration and crash violently into the back of your car.