No, the red star in the image you sent does not have rotational symmetry. Rotational symmetry means that a shape can be rotated about a center point and look exactly the same at certain angles. The star in the image looks different when it is rotated, so it does not meet this condition.
The star has reflectional symmetry, as you can flip it along a vertical or horizontal line and it will look the same. However, this is not the same as rotational symmetry.
A shape has rotational symmetry if it can be rotated by some angle, other than 0°, and look exactly the same.
The red star in the image has five points. If you rotate it by 72° (which is 360° divided by 5), it will not look the same. It will be rotated to a different position, but the points will not be in the same places.
This is true for any angle that you try to rotate the star by. Therefore, the red star does not have rotational symmetry.