Yes, oversized tires can cause Jeep steering wander. Larger tires have a larger contact patch and higher rolling resistance, which amplify existing looseness in the steering. They're also more sensitive to road crown, so your Jeep drifts toward the low side. Incorrect alignment after a tire upgrade is a common cause.
Steering wander is different from death wobble — it's not a violent oscillation but a persistent drifting that requires constant small corrections to hold a straight line. Oversized tires often expose alignment and steering component issues that were present but subtle with the stock tire size. The heavier rotating mass also increases the load on the tie rod ends and the track bar, which can accelerate wear and reduce steering precision over time.
If you're running oversized tires and noticing that your Jeep doesn't track straight without constant input, there are usually a few things to check: alignment settings appropriate for your lift and tire size, toe setting in particular, the condition of your tie rod ends and drag link, and whether any steering components have developed noticeable play. Proper alignment by a shop familiar with lifted Jeeps — rather than a generic alignment spec — makes a significant difference. Hoover Street Auto Repair in Ann Arbor has experience with modified Jeeps to set your alignment correctly for the tires and lift you're running, so you're not fighting the steering wheel on every drive.