I can give you three answers to the titular question:
First, we have no idea. The Bible says nothing about it, nor do any extra Biblical sources. There are, obviously, no human remains.
Scripture doesn't say much beyond Isaiah 53:2, which tells us he had no beauty or majesty to attract us. Early depictions often showed him without a beard. As a semitic man of his time, he likely had dark hair, dark eyes, and an olive complexion. Jerome, Augustine, and Aquinas believed he was handsome and had a regal bearing, but this is theological idealism rather than data.
Second, there's speculation. Based on the limited number of remains studied and notions about diet in 1st century Judea, he might have fallen somewhere around 5'5-6" tall. Averages are slippery things, however, particularly when they are based on millenia-old bones.
The most notoriously obnoxious speculation came from medical artist Richard Neave and a team forensic anthropologists, who did facial reconstruction on a random 1st century Middle Eastern skull and claimed it was "the true face of Jesus" with a chutzpah that would have shamed P.T. Barnum. Its boosters call it "the most accurate likeness ever created." This balderdash surfaced about two decades ago, made headlines, continues to be used, launched a million click-bait ads, and has literally no—none, zero, zilch—evidentiary value. Oh, and they decided he was 5'1". Why? How? Science!
Finally, there’s what the relics tell us.
The Man in the Shroud
I often debunk things here at WeirdCatholic.com, which is a result of researching as carefully and thoroughly as possible. This draws a lot of flak from the credulously pious, but I will always insist that our heritage has real value whether it is based in legend or verifiable history.
There are two relics which, after decades of reading and research, I believe are genuine: the Sudarium of Oviedo and the Shroud of Turin. I also agree with Ian Wilson that the object called the Mandylion was most likely the Shroud folded to display the face, and not a seperate relic.
I'm not going to linger on the authenticity of Shroud right now. You're either a Shroudie and will proceed to the rest of the post, or a skeptic and will consider this all nonsense.
What does the Shroud say about the height of Jesus?
The cloth of the Shroud is 437 cm long by 111 cm wide: roughly 14'3"x3'7". It would have been folded over double into two sections slightly more than 7' long each.
The relic has been extensively studied over the years, most recently using 3D imaging technologies, and new information continues to emerge. Giulio Fanti, a professor of mechanical and thermal measurements at the University of Padua, reported on his observations in 2018, and claims the figure on the Shroud would have been a robust, well-built man of approximately 5'10" in height, which would have made the Lord above the average size for the time.
Sculptor Sergio Rodella has used recent data to produce a model of the figure in the Shroud (shown at the top of this post) which is the most accurate 3D rendering to date.
So, there’s your answer: Jesus was 5 feet, 10 inches tall according to the Shroud of Turin. News you can use!
Also, He loves you and wants you to follow Him.
Exactly the same height as me!
Exactly my height, for whatever it's worth.