Efficient as in "time" or efficient as in "best stats"?

You can get it relatively effortlessly by doing your daily expert roulette until tome capped for the week and doing a few extras for law stones at the side until you get iLvL 170, at which point you want to farm your weekly Alexander drops. Bolts and chain give a quick iLvL boost because you can exchange them for an accessory directly, the other items require two or more before you get your upgrade.

If it's just the iLvL, you can get a 200 ring from esos, a 190 ring, bracelet and collar from Alexander, 190 gloves and full 170 rest in one week. That would put you at pretty exactly 180 unless I miscalculated.

Generally, people will advise you to upgrade your weapon to Eso first, not the ring, though.