Petra is known in the Bible (KJV) as Seir (Genesis 32:3), Sela (Isaiah 16:1-2), Selah (2 Kings 14:7), and Joktheel (Joshua 15:34 and 2 Kings 14:7).

Both Petra and Sela mean ROCK.

It is uncertain who the original builders of Sela/Petra were but the 18+ foot high door may indicate that one of the races of giants may have had a hand in the original construction.
(Smith's Bible Dictionary)

Genesis 6:2
That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.

Genesis 6:4
There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.

This documents the fact that the giants (half breed human/angel offspring) could very well have built this city, this could have happened either before or after Noah's flood. This is indicated by the phrase "and also after that" in Genesis 6:4 above. The Strong's Concordance defines "Horites" #2752 Hebrew."

In Genesis 14:5-6, the Bible describes the fallen angels and their offspring and gives the locations that they lived in.

Genesis 14:5-6
5 And in the fourteenth year came Chedorlaomer, and the kings that were with him, and smote the Rephaims in Ashteroth Karnaim, and the Zuzims in Ham, and the Emims in Shaveh Kiriathaim,

6 And the Horites(#2752) in their mount Seir, unto El-paran, which is by the wilderness.

OT:2752
Choriy (kho-ree'); from OT:2356; cave-dweller or troglodyte; a Chorite or aboriginal Idumaean:
KJV - Horims, Horites.

OT:2356
chowr (khore); or (shortened) chor (khore); the same as OT:2352; a cavity, socket, den:
KJV - cave, hole.

OT:2352
chuwr (khoor); or (shortened) chur (khoor); from an unused root probably meaning to bore; the crevice of a serpent; the cell of a prison: -hole

It also seems that some part of Petra may be where the "cave" that Lot and his two daughters took shelter in just after God overthrew Sodom and Gomorrah.

Genesis 19:30
And Lot went up out of Zoar, and dwelt in the mountain, and his two daughters with him; for he feared to dwell in Zoar: and he dwelt in a cave, he and his two daughters.

Genesis 19:37-38
37 And the firstborn bare a son, and called his name Moab: the same is the father of the Moabites unto this day.

38 And the younger, she also bare a son, and called his name Benammi: the same is the father of the children of Ammon unto this day.

The Bible also states that the children of Moab and Ammon lived in Petra. Lot's two daughters each gave birth to the patriarch of each of these tribes.

Isaiah 16:1-2
16:1 Send ye the lamb to the ruler of the land from Sela to the wilderness, unto the mount of the daughter of Zion.

2 For it shall be, that, as a wandering bird cast out of the nest, so the daughters of Moab shall be at the fords of Arnon.

Seir/Sela was once the home of the Edomites

Deuteronomy 2:12
The Horims also dwelt in Seir beforetime; but the children of Esau succeeded them, when they had destroyed them from before them, and dwelt in their stead; as Israel did unto the land of his possession, which the LORD gave unto them.