I have two pick-up trucks.  One does 65 mph at about 1500 rpm and gets
20 mpg.  The second truck with the same size engine and make does 65
mph at 2000 rpm and gets 15 mpg.  The difference is the rear-end
ratio.  The question is, can I get betrter fuel milage with the second
pick-up by buying a tire with a circunmference about 20% greater?

I am going to say you can't answer this question in the real world
with the current information, though there is possibly a mathematical
answer someone may be looking for if this is some kind of homework
question.

Assuming you mean to go from 15mpg to 20mpg with a truck you actually
have, I think 33% bigger is the number to ask about (15 miles plus 5
miles, 33.33...% of 15, = 20 miles).  20% doesn't even add up as a
theory, though I don't know if you actually have room for a 33% larger
tire.

But even then, you can't tell for sure.

The input and output efficiency of an engine is not in perfect
proportion through the rpm range, and they will usually have a narrow
range in which they work best. Matching the mpg of truck #1 might be
more likely if both trucks have the same engine, just different
ratios. Normally we would assume this as a hypothetical, but if this
is real you very well may have different engines, or even the same
engines in different conditions.

You can't ever get completely "free" energy out of anything, so larger
tires only help if the current configuration is wasting energy for
some reason, like the top gear being too low for your intended use.
You are fixing a problem, not adding free mileage from nowhere. Here
are some "problems" you might be able to fix with a higher ratio:

Vehicle was made for more stopping and going than you actually do.
Vehicle was made for a lower top speed, or lower average speed, than
you are traveling at.
Vehicle was geared for lots of towing/hauling, but you drive it empty.

If you do a lot more traveling at 65 than the manufacturer assumed,
you might benefit from a ratio that does better at 65 than 55.  If you
actually use the truck as the manufacturer expected, you might save
gas at 65 mph only to waste it at 5 mph, or you might actually lose
mileage on average.  Make sure truck #2 doesn't already struggle at
1500 rpm in any gear.

It's possible it could help. Most passenger vehicles have a slightly
low top gear, and at high speeds are running a little high with rpm's.
But don't be certain you can get it to 20, you will be disappointed. 
Also be prepared for nothing.  I wouldn't spend my last $300 trying to
do it.

You probably would get better mileage. The proper way would be to
change the ratio at your differential, rather than the tires. Some
call them 'highway gears'

If the only difference between these two trucks really is the rear-end
gear ratio, then you will *absolutely* get 33% better gas mileage by
going to the 33% larger-diameter tires. Everything in the powertrain
will be running at the same speed, between the two trucks, except for
the rear axle speed, which will be lower in the truck with the great
big tires in the rear. That lower axle speed can only be good for gas
mileage.

Oh wait. 33% bigger tires in the rear means the back end of the truck
will be what, maybe 3 inches higher in the back? There goes your
higher mileage, all lost to bad aerodynamics.  ;)