The following directions are taken from the Coronado National Forest website.
From Tucson, drive east on I-10 for 39 miles to Exit 297, the Mescal Road exit. Drive north on Mescal Road for 16.4 miles until you reach Forest Road 4408. Mescal Road becomes Forest Road 35 after it enters the Coronado National Forest. Turn left and drive 0.4 miles through a gate to a parking area with large Sycamore trees. The trail starts on the opposite side of the creek and follows a 4WD road 1.5 miles to the single track.
The Turkey Creek access to Mica Mountain allows for more of a wilderness experience. This is only a brief summary of the trail. Check with the park rangers for more detailed directions or maps.
From the trailhead parking area at the end of Forest Road 4408, start hiking up the Turkey Creek Trail #34. The land is open and grassy here, but you'll enter the trees higher up. You'll have a good view of Rincon Peak from time to time. After about two miles or so, you will enter the Saguaro National Park. Continue on the trail as it heads up the mountain into the trees. You will soon start hitting a maze of trails up here: the Deerhead Spring Trail, the Switchback trail, the Bonita trail, the Mica Mountain trail, and possibly others depending on your route. I was with someone who knew the way, so I just followed, but there are a lot of trails up here. We also took a shortcut that cut a mile or so off of our hiking route. There are two backcountry camps in this area if you want to camp: Manning Camp and Spud Rock. I wouldn't go up this way unless you're certain you know the way and have a good trail map, otherwise you might get lost. Unlike the west side of the mountain, the trail signs on the east side don't always indicate the route to the summit of Mica Mountain. They only indicate other trails, so unless you know what trails you want to be on, you may not find the summit. It's probably about a 20-mile round trip with 5,000' of elevation gain from this side of the mountain, but that could vary depending on your route.