I don't know if such a font exists, but . . .
It's a Latin script often called Black Letter or Gothic. You could theoretically just write your own, since that kind of script was originally handwritten.
The trick is that these styles of writing are made with an pen with a wide nib, held at a constant angle of around 45 degrees.
You could try writing Japanese with a pen like that, and it would kind of resemble a Latin script written that way. It's also possible to simulate it using the Calligraphy tool in vector software such as Inkscape, or a calligraphy brush in Illustrator. The problem of course is whether writing made in this way would be readable in Japanese, since Japanese is traditionally written with a brush, and not a western style pen nib.
I'll let you be the judge. Here's an example below. Assuming the following are the correct characters (as I don't read or speak Japanese), I took these from the Wikipeda article, I came up with this. However, I don't know if this will be readable for a Japanese speaker.
For comparison, here's a Latin letter B written with the same pen and style
Edit: Looks like somebody else has already had a similar idea here: this is for Chinese, but the same idea basically. https://www.behance.net/gallery/4850969/Chinese-Gothic - Unfortunately, I couldn't tell if this a downloadable font or not. Perhaps you could contact the author.