Preheat oven to 350 degrees F (175 degrees C). Line a loaf pan with parchment paper; grease and flour the pan.
Sift flour, baking powder, and salt into a large bowl. Whisk yogurt, agave nectar, eggs, blood orange zest, and vanilla extract together in a separate bowl until smooth. Pour yogurt mixture into flour mixture; stir to combine. Fold olive oil into batter until incorporated. Pour batter into prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 50 minutes.
Whisk 1/4 cup blood orange juice and turbinado sugar together in a saucepan over medium heat; simmer until sugar dissolves, 1 to 2 minutes. Pour over warm cake to absorb juice. Cool cake completely, 30 minutes to 1 hour.
Whisk confectioners' sugar with 2 tablespoons blood orange juice to make the glaze. Pour over cooled cake.