Francisco Lindor has been among the very best players in baseball since the All-Star break, and even including his initial slow start at the plate upon being called up, his numbers for the season are excellent. He's batting .308/.347/.437 in 314 plate appearances, with 15 doubles, 7 home runs, and 6 stolen bases (plus way too many sacrifice bunts, but that's a different story), along with great defense at shortstop.
Baseball-Reference has him at 2.8 WAR right now; FanGraphs has him at 2.7. Both of those figures place him second in the American League among all rookies, just a touch behind Houston's Carlos Correa. Correa should be considered a heavy favorite for the award, both because he has more home runs, stolen bases, and RBI, and because the Astros appear to be headed to a division title after years at the bottom of the standings. The next month goes the same way as the last month though, Lindor will absolutely be the more deserving of the two.
In any event, awards aside, Lindor is having one of the best rookie campaigns Tribe fans have seen in years.
During the last half century, the clear choice for top rookie season for the Indians is Kenny Lofton, who hit .285/.362/.365 in 651 plate appearances back in 1992 (before offense exploded), with 66 stolen bases in 78 attempts, and good defense in center field. BR pegs that season at 6.6 WAR, while FG has it at 5.8. Both those numbers are nearly double the second-best figure among Tribe rookies in the last quarter century.
Lindor isn't going to reach that level, but he's built a solid case as the best Indians rookie since Lofton.
Who have the team's other top rookies been during that time?
Wayne Kirby (1993)
Kirby hit .269/.323/.371 in 511 PA, with 8 home runs, 17 stolen bases, and a wRC+ of 87. Those aren't good numbers, but he played very good defense in the outfield. BR has him at 3.2 WAR; FG has him at 2.5 WAR. Kirby finished 4th in AL ROY voting Notably; Tim Salmon was the winner that year. Also, Kirby was 29 years old during his rookie campaign.
Manny Ramirez (1994)
Ramirez hit .269/.357/.521 in 336 PA, with 22 doubles, 17 home runs, and a wRC+ of 120. BR has him at 1.6 WAR; FG has him at 1.5 WAR. Neither of those totals stacks up with most of the other WAR figures for these players, but keep in mind that the 1994 season ended 49 games early, likely costing Manny ~1 WAR. He finished 2nd in AL ROY voting, behind Bob Hamelin, who eventually totaled only 488 fewer HR than Ramirez.
Chad Ogea (1995)
Assessing Ogea's rookie season is largely a matter of weighing the merits of what goes into Baseball Reference's version of WAR against what goes into FanGraphs' version. In 106.1 innings, Ogea posted a 3.05 ERA, good for an excellent 154 ERA+. HIs peripherals weren't nearly as good, and his FIP was 4.22. BR has him at 3.2 WAR. FG has him at 1.5 WAR.
CC Sabathia (2001)
In 180.1 innings, Sabathia put up a 4.39 ERA, good for a 102 ERA+ in that very high-scoring season. He also went 17-5, which says a lot about how good the Tribe offense was that season, and less about Sabathia's own performance, but is a very pretty record. BR has him at 2.9 WAR; FG has him at 2.7 WAR. He finished 2nd in AL ROY voting, somehow snaking one 1st-place vote away from the obviously more deserving Ichiro Suzuki.
Casey Blake (2003)
Blake hit .257/.312/.411 in 621 PA, with 35 doubles, 17 home runs, and a wRC+ of 91. He also played very good defense at third base. Like Kirby, Blake was 29 years old in his rookie year. In fact, he turned 30 before the season ended. BR has him at 3.5 WAR; FG has him at 2.0 WAR, which represents a pretty big difference of opinion for a position player.
Jody Gerut (2003)
Gerut hit .279/.336/.494 in 525 PA, with 33 doubles, 22 home runs, and a wRC+ of 117. He also played strong defense in the outfield. BR has him at 2.8 WAR; FG has him at 3.2 WAR. He finished 4th in AL ROY voting. (Angel Berroa was the winner, giving the Royals another ROY who went on to a very mediocre career.)
Ben Francisco (2008)
Francisco hit .266/.332/.438 in 499 PA, with 32 doubles 15 home runs, and a wRC+ of 106. He had a strong arm, but his overall defense wasn't good. BR has him at 2.3 WAR; FG has him at 1.7 WAR. He didn't receive mention in AL ROY voting.
Carlos Santana (2010)
Santana hit .260/.401/.467 in 192 PA, with 37 walks, 13 doubles, and a wRC+ of 140. His rate stats on offense were by far the best of any player on this list, but he also had by far the least playing time. BR has him at 2.0 WAR; FG has him at 1.8 WAR.
It's not an easy decision, but my choice for best Tribe rookie season since Lofton is Jody Gerut. He played close to a full season, and did very well on both offense and defense. Lindor is very close to him though, and with a month left to go in the season, I expect Lindor will pass him.