No, he won't be able to "file the taxes for the property" if you put it in your revocable trust. The property now belongs to your son. You cannot put his property in your trust unless you buy it from him or he gifts it to you. If you buy the property from him it will be a taxable transaction. If he sells it to you at less than market value, that will be a gift of the difference between the price you pay and the market value. If he gifts the property to you outright, then he will need to file a Gift Tax Return. (Did you file a gift return when you gave the property to your son?) Once in your living trust, you will report the income and expenses for the rental property on your tax return, not your son's.
to do want you want would require the assistance of a real estate lawyer since you don't own it and since your son's consent would be needed. In addition, there are major gift tax and income tax issues. For example, what you gifted to him would now have to be gifted d back to you. The IRS may deem the original gift invalid and make you responsible for reporting the rental activity on your taxes for the original acquisition date. As the grantors to the revocable (grantor) trust, you would be the ones under the tax laws required to report the activity on your tax return even if he got the rent and made all the payments. (possibly requiring annual gift tax filings)
I don't see any reason to do what you suggest and do so will complicate tax compliance for everyone.