Answer
The angular momentum of the Earth due to rotation about its axis is $~7.04\times 10^{33}~kg~m^2/s$
Work Step by Step
We can find the angular speed of the earth as it rotates:
$\omega = \frac{\Delta \theta}{\Delta t}$
$\omega = \frac{2\pi~rad}{(24)\cdot (3600~s)}$
$\omega = 7.27\times 10^{-5}~rad/s$
We can find the angular momentum of the Earth due to rotation about its axis:
$L = I~\omega$
$L = \frac{2}{5}MR^2~\omega$
$L = \frac{2}{5}(5.97\times 10^{24}~kg)(6.37\times 10^6~m)^2~(7.27\times 10^{-5}~rad/s)$
$L = 7.04\times 10^{33}~kg~m^2/s$
The angular momentum of the Earth due to rotation about its axis is $~7.04\times 10^{33}~kg~m^2/s$.
