Yes—an iPhone app such as Theodolite can store orientation information with the image. According to the community answer, it writes values like vert_angle_deg and horiz_angle_deg into the photo’s Image Description metadata, and can also overlay those readings on the image.

However, there’s an important limitation: readings become unreliable when the camera is aimed near the zenith (straight up). The reported vertical and horizontal angles may vary a lot between nearly identical shots, likely because phone compass/orientation sensors are sensitive to nearby metal or magnetic interference.

So in practice:

• Yes, tilt/elevation metadata can be recorded on iPhone.
• No, you should not assume it will be highly accurate for straight-up shots.

If you need dependable zenith measurements, a physical mount or gimbal to keep the camera pointed upward will likely be more reliable than phone sensor metadata alone.