The word ἄρτιος (artios) is not found elsewhere in the New Testament or the Septuagint, but it is reasonably well-attested in Classical Greek literature; LSJ provides many examples. BDAG gives:
pertaining to being well fitted for some function, complete, capable, proficient = able to meet all demands
Although the word is a hapax within the Greek Bible, there is a related set of words, also derived from ἀρτίζω (artizō), with attestation here. These add the prefixes εκ- or κατα-, but the usage pattern indicates a closely related (if somewhat amorphous) meaning. NIDNTTE helpfully gives "concepts" that characterize the word group:
Arrange; Goal; Good; Make; Prepare1
One such term is used in this very same verse: ἐξαρτίζω (exartizō; "to finish, complete, equip"):
ἵνα ἄρτιος ᾖ ὁ τοῦ θεοῦ ἄνθρωπος, πρὸς πᾶν ἔργον ἀγαθὸν ἐξηρτισμένος
so that the the man of God might be artios, exērtismenos toward every good work
Thus, although the verse does not repeat precisely the same word, it does use a closely related word, this with the nuance indicating "directionality", i.e. specific to an object: "every good work". Exartizō is also used also at Acts 21:5, lit. "our days were completed"
More common is καταρτίζω (katartizō), occurring 13 times in the New Testament. Most often it refers to attainment of or restoration unto spiritual maturity (e.g. 1 Cor 1:10, Gal 6:1, 1 Thess 3:10, Heb 13:21, 1 Pet 5:10). Also from NIDNTTE:
It is clear that the words in this group were appropriated by the NT writers, especially Paul, as ideally suited to express concepts related to Christian growth, whether in the context of problems that needed to be remedied, or in connection with training for service, or more generally to encourage spiritual maturity.
2 Tim 3:17 fits nicely in this framework. Scripture has been given to the "man of God" in order to fully prepare him with the principles necessary to approach every "good deed".
OP additionally asks:
[W]hy does the KJV translate it "perfect"?
I think this is most likely an example of archaic (?) English usage that may be unfamiliar to us. Several of the available meanings from Merriam Webster seem to me consistent with the above discussion:
3b. lacking in no essential detail: complete
4. obsolete: mature
You may have noticed that LSJ didn't have a problem glossing ἄρτιος (artios) using "perfect". The emphasis on faultlessness that may be felt in modern parlance was likely not the intention of either KJV or LSJ.
Although I think it's a less likely explanation for the KJV rendering, it's worth mentioning that there is one manuscript – Codex Claromontanus – that reads not ἄρτιος (artios) in 2 Tim 3:17 but τέλειος (teleios).2 The manuscript can be viewed on the Bibliothèque Nationale site. See line 7:
ΙΝΑ ΤΕΛΙΟϹ Η, followed inline by the correction in a different pen:
ΑΡΤΙΟϹ Η. This manuscript is a Greek-Latin diglot, and the reading was possibly influenced by the Vulgate: perfectus sit homo Dei....
1. "ἄρτιος" in New International Dictionary of New Testament Theology and Exegesis (NIDTTE). Ed. Moises Silva (Zondervan, 2014), 1:408-410.
2. An adjective well-known from Matt 5:48, 1 Cor 13:10, Jas 1:17, 1 Joh 4:18, etc., consistently translated using "perfect" in the KJV. It seems to be misspelled in the manuscript (telios rather than teleios, possibly influenced by the correct word, artios?).