I don't know if such a font exists, but . . .
It's a Latin script often called Black Letter, Gothic, or Fraktur. 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 calligraphic pen nib.
I'll let you be the judge. Here's an example.
