The correct answer is $\boxed{\text{A. }-4.33 \text{ diopters}}$.
The power of a lens is given by the formula:
$$P = \frac{1}{f}$$
where $f$ is the focal length of the lens in meters.
The focal length of a convex lens is positive, so the power of a convex lens is also positive.
The image formed by a convex lens is real and inverted when the object is placed between the optical center and the focal point of the lens.
In this case, the object is placed at a distance of 12 cm from the optical center, which is less than the focal length of the lens. Therefore, the image formed is real and inverted.
The distance between the object and the image is given by the formula:
$$d_o + d_i = f$$
where $d_o$ is the distance of the object from the lens, $d_i$ is the distance of the image from the lens, and $f$ is the focal length of the lens.
In this case, we know that $d_o = 12 \text{ cm}$ and $d_i = 25 \text{ cm}$. Substituting these values into the formula, we get:
$$12 \text{ cm} + 25 \text{ cm} = f$$
$$f = 37 \text{ cm}$$
The power of the lens is then given by:
$$P = \frac{1}{f} = \frac{1}{37 \text{ cm}} = -0.027 \text{ m}^{-1} = -4.33 \text{ diopters}$$
Therefore, the power of the convex lens is $\boxed{\text{A. }-4.33 \text{ diopters}}$.