Add noise to gradient photoshop
Solution 1:
Filter > Noise > Add Noise...
EDIT: If it's on a layer style (good info to add), you can right click the FX button next to the layer, and select "Create Layers". This will split the gradient overlay onto its own layer. Then apply a noise filter to that layer.
Solution 2:
From your comment on SO I know you are using a layer style. You should specify this as this is NOT the only way to get a gradient.
A gradient layer style will be applied OVER the layer. Filter > Noise applies the noise to the layer which is then being covered by a layer style.
There are several ways to do this with a layer style, here are a couple:
Create a new empty layer, then select both layers, right click and select "merge layers" this will rasterize your layer style. You can now add the noise filter directly to it.
Add a layer mask, Layer>layer mask>reveal all. Then apply the noise filter to the layer mask.
There are plenty more ways, these are just the 2 that popped into my head at the moment.