Sure, although it depends heavily on your talents, language, and most of all luck (or alternatively, massive amounts of money).
You basically have three paths:
- Get published as a Light Novel or Webnovel, and get a manga adaptation.
- Become a story writer for a manga.
- Commission someone to draw your story into a manga.
for all intents and purposes, to break into 1 or 2, you will need to write in Japanese (or to a lesser degree, Chinese or Korean) and post your work to a fiction posting site like 小説家になろう or pixiv. Ride the trend (currently it would be Isekai), promote your work on the likes of Japanese Twitter, and with a massive amount of luck (with the tosh that gets published these days, I am not sure talent is that necessary), you will rise above the massive sea of LN writer hopefuls to get selected for a publishing deal - and if you are even luckier and sell well, you might get a manga adaptation.
I am not going to say it is impossible to get a manga adaptation as an English writer, but Japanese publishers really have no reason to look for talent elsewhere when there are thousands of amateur writers committing millions of words in their own language online for free hoping for that big publishing break, even at bottom barrel rates.
Submitting your work to publishers directly rather than online is of course an option, but that seems to have been mostly phased out for the online model.
Lastly, for 3, if you have plenty of money and don't care about actually selling your work, you can just commission an artist or (amateur or freelance) mangaka to draw your story (although it will likely cost you an arm and leg for what is in essence a vanity project)
EDIT: this is a response to OP's comment that became far too long for its own good, so I am adding it here. Mods, please tell me if this isn't appropriate.
I will be frank; it is nearly impossible for an English writer to break into the Japanese manga market directly, regardless of talent.
The manga market is absolutely saturated with talented hopefuls (most of whom will never even get a oneshot published, let alone a series), and the LN market even more so. Thus like I have said, Japanese publishers have very little reason to turn to foreign talent - why risk the legal and communication pitfalls when there are hundreds of Japanese who are eager to replace them for little recompense?
I'd say that the best chance for a foreign writer to get published in Japan is to be either A. To get an internationally bestselling book or B. work with an artist (as @Mary has said) to get a bestselling comic, and have a Japanese publisher pick up rights for localization of your work.
For A., there are cases of foreign books getting a manga adaptation (e. g. The Unwomanly Face of War. Note that this book is by a Nobel Literature prize-winning author), but they are very rare, and generally reserved for the bestselling of books or classics in the public domain.
For B, while foreign comics (e.g. Chinese and Korean webtoons and Western comics) have recently made decent headway in penetrating into the Japanese market, most of them deviate signifcantly from the cliches and customs of the manga genre (and are successful at least partially thanks to that difference).
If you really want keep it limited to manga form, I suppose you could find a mangaka who is willing to collabrate with you via both translating and drawing your work, but that honestly isn't much more likely than getting a bestselling book.
TL;DR: It is really bloody difficult, especially if you can't write in Japanese.