To apply a brush texture to a vector in Adobe Photoshop follow these steps.

Select Background

Start with whatever background you want. In this case we are using a blue canvas. Set your background on it’s own layer and lock the layer. We won’t be touching this for the rest of the tutorial.

Select Brush

Open the brush window and select whichever brush you would like to apply.

Apply Brush

Apply the brush so that the whole stroke is inside the canvas. If it goes over the edge it will clip. You can resize and rotate the brush stroke later.

Name Brush Layer

Name your new layer.

Adjust Brush Layer

Using the selection tool you can rotate and resize the stroke however you want.

Select Vector

Go into Illustrator and copy your vector of choice.

Paste Vector

Back in Photoshop, select the Brush layer you just made and then paste (ctrl+v) the vector you just copied in Illustrator. Photoshop will ask you what format you would like the vector pasted as. Select Path.

Apply Brush to Vector

The path will be applied to the brush stroke.

Unlink brush from vector

You can click the chain icon to unlink the brush stroke and the vector path so that the stroke and be adjusted independently inside of the path. This will let you fine tune the appearance of the stroke on the vector.