It is possible, as other comments suggest, to purchase either the Koin変体仮名 fonts or the Mojikyo (文字鏡) suite for use in word-processing (Office Word, TeX). Koin変体仮名 is also available for free but, obviously, not all the glyphs are usable. As for Mojikyo, there seems to be a free version which can be obtained as follows:
1) The fonts from http://www.mojikyo.org/#TTF_download : download one by one, extract them as these are archived.
2) Go to https://tinyapps.org/blog/windows/201002130700_mojikyo_character_map.html where all the necessary instructions can be found (including step 1).
The drawback is that you can't just type in hiragana and expect Mojikyo Character Map or your word processor to convert them into hentaigana. The mapping issue might be one of the reasons a paid version exists. Hentaigana inventory is also limited (although generous enough for most purposes, I estimate there are more than 200 glyphs).
These two solutions appear to be the more easily found ones. So far I was unable to find others. Lastly, even though I use the Character Map myself, I think it necessary to add that by downloading and installing the files you proceed at your own risk.