I think generally we use kanji 私 but sometimes it's written in hiragana in poetry or something because it looks a bit more soft. However, mixing them up in one note or poetry doesn't look good. If you start wiring it in kanji, please keep using the same way in one note. I hope this was helpful.

The hiragana for it is わたし You will notice a lot of girls in manga say あたし

私 :)

generally I is written as the kanji, however certain words can be written in kana alone even if there is a kanji for it.