Not sure if there is a way to do this by explicitly providing a kwarg to plt.quiver, but a quick work around would be like this:

original plot

x = np.arange(10)
y = np.arange(10)
xx, yy = np.meshgrid(x,y)
u = np.random.uniform(low=-1, high=1, size=(10,10))
v = np.random.uniform(low=-1, high=1, size=(10,10))
plt.quiver(xx, yy, u, v)

normalized plot

r = np.power(np.add(np.power(u,2), np.power(v,2)),0.5) #could do (u**2+v**2)**0.5, other ways...
plt.quiver(xx, yy, u/r, v/r)

this just normalizes the u and v components of the vector by the magnitude of the vector, thereby maintaining the proper direction, but scaling down the magnitude of each arrow to 1