Yes, injured Woman! rise, assert thy right! (1)
The first line addresses "injured Woman." By making "Woman" singular and by capitalizing it, Barbauld apostrophizes some universal, oppressed woman. It can apply to any woman, anywhere. So any woman who reads or hears this poem could feel that it's a direct call to arms to her.
Go, gird thyself with grace; collect thy storeOf bright artillery glancing from afar; (9-10)
Women are told to put on their armor, but all they get in the way of armor is grace. That's not going to stop bullets, but maybe the speaker thinks that if women have enough grace, they won't need to stop bullets—no one will want to shoot at them at all.
Soft melting tones thy thundering cannon's roar,Blushes and fears thy magazine of war. (11-12)
Women don't get much in the way of real weapons, either. Instead of cannons and military storehouses ("magazines of war"), they get to use a soft tone of voice, blushes, and fears. Again, these are not things that are going to stop an oncoming army, but according to the speaker, these are uniquely feminine weapons. Women just need to learn to use them more effectively. It's kind of weird, though, that in a poem about women's rights, Barbauld claims that women should conform to traditionally and stereotypically feminine ideals. Do you think she's being ironic?