I'm new to the photography stack exchange and would like to participate in the Photo of the Week contest. However, I'm also new to photography and only recently got a DSLR camera so I haven't taken many photos with it. Is it okay if I submit some photos I've taken using my phone until I have more taken on my DSLR?
They always have been. I see no distinction between a phone, a DSLR, a film camera or even a Box Brownie in this respect.
It's the end result that counts.
I even once won the old 'Image of the week' which was the predecessor of the current competition with a photo taken on an iPhone
I can't direct-link it because at the time the original winner was then deleted from the list & placed in a separate Hall of Fame list.
Image of the Week “Hall of Fame” (2017 Archive) then scroll down to 14 August 2017 if you want to see it.
Absolutely, they are allowed. A photo is a photo. While many of us might personally be snobs about how we take our own photos with respect to film, dedicated digital SLRs or mirrorless, vs. smartphones, I dare say that everybody here respects a good photo, regardless of the imaging source.
Indeed, in many ways, great smartphone photos are even more impressive, considering some of the restrictions they have.
(Counterpoint: recent smartphones with computational photographic technology makes taking great photos easier, in some ways easier than with traditional dedicated cameras. But that's an entirely separate conversation)