The Centaur race published in the Mythic Odysseys of Theros and Guildmaster's Guide to Ravnica books is considered size Medium. However, due to the Equine Build trait, it counts as one size larger when determining your carrying capacity and the weight you can push or drag.
Does this mean the Centaur player race can carry a Medium-sized rider?
A reasonably strong Centaur should have no issue physically carrying a Medium creature.1 With only a Strength score of 10, a centaur has a carrying capacity of 300 pounds, increasing by 30 pounds for each point added to their Strength score. But being carried in this way does not confer the benefits of having mounted the centaur, which seems to be what is being asked, as evidenced by use of the word "rider".
The centaur's Equine Build trait specifies which things the centaur is considered Large for:
You count as one size larger when determining your carrying capacity and the weight you can push or drag.
The rules for mounted combat say:
A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount, using the following rules.
Since being mounted is not mentioned in Equine Build, you are still considered Medium for the purposes of what size creature can mount you - Small or smaller.
This is definitely rule-as-intended. In the Unearthed Arcana version of the Centaur race (.pdf link), the Equine Build trait included the following text:
Finally, a Medium or smaller creature can ride on your equine back if you allow it. In such a situation, you continue to act independently, not as a controlled mount.
This portion of the feature was removed for the official release of the Centaur playable race in Guildmasters' Guide to Ravnica.
There is an optional rule in the Dungeon Master's Guide that can give us some guidance, but I must emphasize, everything that follows is entirely at the DM's discretion.
The DMG has an optional rule for climbing onto a bigger creature (p. 271):
a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb. [...] While in the target’s space, the smaller creature moves with the target.
So it will be up to the DM to determine if a centaur is "suitably large". It also has some details about contested ability checks, but those shouldn't be an issue for a willing centaur.
From here, it is up to the DM. If your table is going to go this route, this should be viewed as a house rule guided by an optional rule from the DMG, and your table should decide together what it looks like, and write it down so it can be consistently adjudicated.
Personally, I would recommend against this, as this is clearly contrary to the intent of the rule.
1 Thanks to user SirTechSpec for pointing out this important distinction.
