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The reincarnate spell replaces your racial traits, within which ability score increases are included. Is a racial ability score increase capped at 20 like a class ASI?

For example, if I have 20 Charisma as a Half-Orc and am reincarnated into a Half-Elf would I then have 22 Charisma?

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Ability scores have a maximum of 20 for player characters.

From the first chapter in the Player's Handbook, section Beyond 1st Level:

[...] Some of these features allow you to increase your ability scores, either increasing two scores by 1 each or increasing one score by 2. You can't increase an ability score above 20. (PHB, 15)

But, one might argue, this only applies to ability score increases from leveling up. So what about your case, when someone gains a racial ability that increases their ability score while they are already at 20?

From Chapter 7: Using Ability Scores in the Player's Handbook:

A score of 10 or 11 is the normal human average, but adventurers and many monsters are a cut above average in most abilities. A score of 18 is the highest that a person usually reaches. Adventurers can have scores as high as 20, and monsters and divine beings can have scores as high as 30. (PHB, 173)

Adventurers, such as a player character, can go as high as 20, but no higher.† To my knowledge, level 20 Barbarians are the sole exception thanks to the Primal Champion trait, which increases their maximum Strength and Constitution (as well as the scores themselves) by 4.

In your case, rules as written, a Half-Orc with a 20 in Charisma who is reincarnated into a Half-Elf would still be at 20 Charisma.

As always, there are exceptions to the rule. There do exist magical means to increase ability scores above 20; for example, the Tome of Leadership and Influence for Charisma.

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  • \$\begingroup\$ @Medix2 Yes, which is addressed in my answer. "Outside of some sort of magical effect"... \$\endgroup\$ – Baron May 13 '18 at 20:05
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    \$\begingroup\$ A bit of a nitpick but inwoikd say "capped at 20 for all abilities." Stats (aka game staitlstics) include things like HP which is certainly not capped at 20 \$\endgroup\$ – David Coffron May 13 '18 at 20:27
  • \$\begingroup\$ Does everything that can raise something over 20 say so explicitly? \$\endgroup\$ – JollyJoker May 14 '18 at 9:09
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    \$\begingroup\$ @JollyJoker Yes, otherwise it wouldn't raise the cap. \$\endgroup\$ – Baron May 14 '18 at 10:01
  • \$\begingroup\$ @Baron Not everything that raises a stat above 20 also raises the cap. See: Star Card \$\endgroup\$ – Medix2 May 14 '18 at 13:41

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