It means to be called into a room to be reprimanded.
The expression call on the carpet has been in usage since at least 1881, when it appeared in a glossary of words and idioms published by the English Dialect Society. The entry is actually for carpet, used as a verb, meaning "to summon for the purpose of enquiry or reprimand" (a usage that the Oxford Dictionary of Idioms dates to the mid-1800s). The definition then elaborates with the related idiom:
To be 'called on the carpet' is equivalent to receiving a scolding, the metaphor being taken from a servant called into the presence of the master or mistress from an uncarpeted into a carpeted room.
In A Fine Kettle of Fish, and Other Figurative Phrases, lexicographer Laurence Urdang offers a similar explanation: It was "said of a servant called into the parlor (a carpeted area) before the master or mistress in order to be reprimanded." The American Idioms Dictionary and Dictionary of American English Phrases, both by Richard A. Spears, update the imagery from master and servant to boss and underling, stating that "The phrase presents images of a person called into the boss's carpeted office for a reprimand."
From https://www.visualthesaurus.com/cm/dictionary/called-on-the-carpet/