--source include/have_innodb.inc

create table t (pk int primary key, a int, key(a)) engine=InnoDB;

set foreign_key_checks= 0;

alter table t add foreign key (a) references t(a);

# Cleanup

drop table t;

ALTER above fails with

ER_FK_NO_INDEX_PARENT (1822): Failed to add the foreign key constaint. Missing index for constraint '' in the referenced table 't'

It's not that surprising that it fails in general – after all, a self-referencing column hardly makes sense – but that it fails with ER_FK_NO_INDEX_PARENT although clearly there is an index.
With explicit ALGORITHM=COPY it succeeds (only producing a warning about an invalid FK in the error log).

Reproducible on 10.2-10.6, including older ones, as well as MySQL 5.7 and 8.0. I didn't check earlier versions.