The first ten prime numbers are:
\[
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
\]
The median of a set of numbers is the middle number when the numbers are arranged in ascending order. Since there are 10 numbers, the median is the average of the 5th and 6th numbers:
\[
\text{Median} = \frac{11 + 13}{2} = 12
\]
Thus, the correct answer is 12.