No male article* shall be on a woman, and a man shall not wear a woman’s garment. Whoever does such practices is revolting to G-d your L-rd (Deut. 22:5)

Rabbi Aryeh Kaplan translates Dvarim / Deuteronomy 22:5 in the following way:
No male article* shall be on a woman, and a man shall not wear a woman’s garment. Whoever does such practices is revolting to G-d your L-rd (- instead of o, was inserted here by the editor, not by Rabbi Kaplan).

Rabbi Kaplan comments:

* male article. Clothing (Septuagint). But this also includes weapons (Nazir 59a), and, according to some, tefillin and tzitzith ( Targum Yonathan ; cl. Eruvin 96a; Orach Chaim 38:3 in Hagah).

Rabbi Moshe Feinstein

In theory, at least according to Rabbi Moshe Feinstein, a woman who wants to fulfill (as extra credit) the mitzva of Tzitzit could do so, if she has a 4 cornered garment that looks different from a male garment*.

Regarding Rabbi Feinstein’s leniency regarding women carrying weapons, see: “Ascending the Temple Mount for the Sake of Saving Lives – Letter 2” – topic 4

Rabbi Moshe Feinstein didn’t tell us to rely upon the government to save us from Murderers and did not say that we should avoid prohibitions by sitting at home and see what Rabbi Neventzal wrote in response in the name of Admo”r ZLLH”H and the Chazon Ish ZT”L

Source of Rabbi Feinstein’s psak on Tzitzit:

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שו”ת אגרות משה אורח חיים חלק ד סימן מט *
איברא דאיכא