It is fairly small, we'd never notice it. Here's how I know. I've seen calculations that say the center of the Earth is 2.5 years younger than the surface of the Earth, simply due to time dilation at the high gravitational potential existing there. (You would be floating in mid air, but you are surrounded by tons of rock thus experience a high gravitational potential.) On the surface of the Earth we only experience about half the gravitational potential since the half under our feet is rock but the half over our heads is air. This is a BIG difference, yet only accounts for 2.5 years in the last four billion.
The amount of gravitational potential energy that the stars around us add is proportional to the average density.
The average density is the amount of mass divided by the amount of space. In our part of the Orion arm the nearest star is 4 light years away. In our exclusive space, half way to the nearest stars, the only mass is the Solar System. The Sun accounts of 99.9% of the mass.
Now look at this volume in reduced scale. We shrink things down until the distance to the nearest star is 300 km. In this model, the Sun is a cubic cm or the size of a grape. A grape is not much mass for a volume of 100 million cubic kilometers.
Therefore: In the arm or out of the arm does not make much difference. Our 2.5 year example would ratio to the same ratio as the cubic cm to 100 million cubic km. Multiplying out we find the time dilation due to being in an arm, over the age of the Earth, is a factor of 1e20. The 2.5 years becomes 8e-13 s.
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