How to generate a degree sequence of a degree distribution
As you mention, the degree distribution follows a power law if the number of nodes of degree $k$ is roughly $N \times C^{-1} k^{-\gamma}$, where $C = \sum_{k = 1}^\infty k^{-\gamma} = \zeta(\gamma)$ (in your case, $C \approx 1.34$). Plugging in your numbers, we want roughly


75 vertices of degree 1.
13 vertices of degree 2.
5 vertices of degree 3.
2 vertices of degree 4.
1 vertices of degree 5.
1 vertices of degree 6.
1 vertex of degree 7.


This gives a total of 98 vertices. You can make it exactly 100 vertices in many ways &mdash; I'll let you think of one. Don't forget that the sum of degrees should be even.

The (potential) problem is that not every sequence is the degree sequence of a graph. Sequences which are realized by some graphs are known as graphic sequences, and are determined by the Erdős&ndash;Gallai criterion. If the resulting sequence doesn't satisfy this criterion, we're in trouble. However, I don't expect it to happen in your case. Indeed, my suggestion above (with 98 vertices) is graphical.