Can I install CWM without rooting my Android Phone?

Yes, for sure you can my friend. You will have to unlock your bootloader for that first.

This will definitely void your warranty but your device won't be rooted, as for rooting first you unlock your bootloader then you flash superuser app onto your device. Henceforth, until you install "superuser" your device will not be rooted.

So you can flash CWN without rooting your device, as it only requires unlocking your bootloader and no superuser installation.

*Unlocking bootloader voids warranty so do be cautious and prudent my friend, but CWM has benefits of its own. The choice is yours.

Hope, I was helpful.

While there is the CM installer which just installs CM without any mess, not many models are supported. Other than that you cant do it without rooting. And once CM is installed your phone gets rooted anyways.

I wouldn't recommend rooting your Android phone as this will void the warranty, but other than rooting it, I don't think you can.