Preheat oven to 200 degrees F (95 degrees C). Line 2 baking sheets with parchment paper.
Combine aquafaba, rose water, lemon juice, and cream of tartar in a large bowl. Beat with an electric mixer until fluffy, 10 to 30 minutes. Increase speed to high and beat, gradually adding confectioners' sugar, until meringue holds stiff peaks, about 10 minutes. Scoop meringue into a piping bag fitted with a round tip.
Pipe small mounds of meringue onto prepared baking sheets.
Bake in the preheated oven, rotating sheets halfway through, until meringues are dry and firm, 1 1/2 to 2 hours. Turn off oven; keep meringues inside until cooled.
