If your factory stock tire size is 265/60R18, your tire O.D. is 30.5"
Your new tire size of 265/65R18 will be 31.6" O.D.
So you're going to be about 1.1" larger in diameter which means your tire will extend into the wheel wells .55" (the radius of the O.D.) less than the thickness of your pinky finger.
That should not cause any issues except maybe (and I mean, not likely, but maybe) in extreme circumstances like completely compressing your tire into the wheel well at full lock might cause light rubbing.
With that small of diameter increase, if you had to you could just go with .5" - 1" spacers which are inexpensive and call it done!