I recently got a flat on one of my front tires. I replaced it with a newer tire that had a little more tread on it than the remaining three tires. After replacing the tire, my car shakes/vibrates when I reach speeds around 65mph. I really don't want to spend the extra money buying another new tire so that the axel has 2 tires with approximately the same amount of tread. I'm wondering: would it be better to rotate all four tires like once a month to help even out the wear more? Or is there anything else I can do other than buy more tires?
my car shakes/vibrates when I reach speeds around 65mph
The tire should not shake, take it back to where you bought it and have them re-balance it. Vibration and heat are enemies of anything mechanical.
would it be better to rotate all four tires like once a month to help even out the wear more?
No. Constantly moving other tires around won't effect that one tire's wear pattern, it will still have the most tread.
You left out a few details. (Why is this important? For example, if you have an AWD vehicle you need to replace all four tires at once to avoid damaging the drivetrain.)
replace tires in pairs, and put the new ones on the rear
