Yes, you should be able to transfer your pension to a revokable living trust.
A living trust has the same federal ID number that you do (your social security number). Any income received by the trust is treated as your income (this will include taxable pension distributions). This is not a vehicle to reduce your taxable income.
Trusts (revokable living or any other kind) are generally estate-planning or wealth transfer tools. You should contact an estate/trust attorney and possibly a CPA who is experienced in estate and trust matters to discuss whether this is a good option for you.
Please note that if you establish a revokable living trust, you will need to either contribute all of your assets to the trust or discuss "pour over" provisions in your will with your estate attorney. If you do not do so, you can create two entities upon your death (the trust, which becomes irrevokable, and your estate), which will make matters much more complex for the trustee and/or your executor.