  Recently, gas giant planets in nearly circular orbits with large semimajor
axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have
investigated orbital evolution in a formation scenario for such planets, based
on core accretion model: i) Icy cores accrete from planetesimals at $\lesssim$
30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire
highly eccentric orbits, and iii) their orbits are circularized through
accretion of disk gas in outer regions, where they spend most of time. We
analytically derived equations to describe the orbital circularization through
the gas accretion. Numerical integrations of these equations show that the
eccentricity decreases by a factor of more than 5 during the planetary mass
increases by a factor of 10. Because runaway gas accretion increases planetary
mass by $\sim$ 10--300, the orbits are sufficiently circularized. On the other
hand, $a$ is reduced at most only by a factor of 2, leaving the planets in
outer regions. If the relative velocity damping by shock is considered, the
circularization is slowed down, but still efficient enough. Therefore, this
scenario potentially accounts for the formation of observed distant jupiters in
nearly circular orbits. If the apocenter distances of the scattered cores are
larger than the disk sizes, their $a$ shrink to a quarter of the disk sizes;
the $a$-distribution of distant giants could reflect outer edges of the disks
in a similar way that those of hot jupiters may reflect inner edges.
