How do you have pKa for a base?
For bases, you can derive the $\mathrm{p}K_\text{a}$ from the $\mathrm{p}K_\text{b}$.

Knowing that 

$$\mathrm{p}K_\text{a} + \mathrm{p}K_\text{b} = \mathrm{p}K_\text{w} = 14$$

Let’s examine ammonia.

Ammonia has a $K_\text{b}$ of $1.8 \times 10^{-5}$.

Taking the negative logarithm, we can derive $\mathrm{p}K_\text{b}$:

$$\mathrm{p}K_\text{b} = -\log( 1.8 \times 10^{-5}) = 4.74$$.

Knowing that $\mathrm{p}K_\text{a} + \mathrm{p}K_\text{b} = \mathrm{p}K_\text{w} = 14$:

We can find $\mathrm{p}K_\text{a}$ by manipulating that expression, thus:

$$\mathrm{p}K_\text{a} = 14 - \mathrm{p}K_\text{b} $$

$$\mathrm{p}K_\text{a} = 14 - 4.74 $$

$$\mathrm{p}K_\text{a} = 9.26 $$

Even in very basic solutions, there will be minute quantities of hydronium ions. By taking the anti-logarithm of the $\mathrm{p}K_\text{a}$, you can derive the $K_\text{a}$.