Moshe Katz's answer is right that you'll have to re-encode the video with it rotated. But actually you already are: your phone probably records H.264 (MPEG-4 AVC). DVD Video requires MPEG-2 — those are two different codecs, thus you have to re-encode.
So, if you can find a DVD creation program that understands orientation metadata (or can be told to rotate the video) you don't have to add another re-encode.
That said, there will probably be loss of quality for two reasons:
- Chroma subsampling
- Wrong resolution
Chroma subsampling. First off, video uses a bunch of tricks to get what is really a high data rate — almost 3 gigabits/second for 1080p@60 — down to a manageable data rate. One of those tricks takes advantage of the human eye being less sensitive to color differences than brightness differences by discarding a lot of the color information. One common method, called 4:2:0 subsampling, takes every 4×2 block of pixels and discards the color information from half of the pixels on the top row and all of the pixels on the bottom row. Why? Well, color is ⅔ of the data — so going from 8 color pixels down to 2 halves the data rate. This does pose a problem with rotating it, though, at least if its been scaled at all. If it hasn't been scaled, it'll hopefully line up (but it will be scaled, see #2) (DVD Video forces you to use 4:2:0, so this is unavoidable).
Wikipedia has a nice graphic in their chroma subsampling article which shows the different methods and what they do to a block, it's about ¼ down the page. Note that Y is the brightness and Cr and Cb are the color.
Wrong resolution. DVD Video requires video to be in several very specific resolutions, the largest on being 720×480 (at least for NTSC; on PAL DVDs its 720×576). If your video doesn't have that resolution then it must be scaled and letterboxed (black border added). So, for example, if your video is 720 pixels tall instead of wide, then it'll be scaled down to be 480 pixels tall, then black borders added left and right to make it a DVD resolution again (probably 704×480, the next one down.)
[There is actually a lot more complexity here; for example, if you try to compute the aspect ratio of 720×480 you'll notice that it's 3:2, which is weird — it's neither 4:3 nor 16:9. That's because DVD pixels aren't square—that same resolution produces both 4:3 and 16:9, depending on a flag on the DVD). Also, part of the 720×480 frame is supposed to be ignored/unused, because analog TV. That is often ignored, but not always.]