Some places have certain restrictions on what you can and can't do on your property but in most places you certainly can have a privacy fence in your front yard and all the way around your house as well.
I have a 6 foot tall privacy fence that sits a foot away from the sidewalk and I have a gate that opens up to lead up to my porch and another gate that opens to go into my driveway.
The town I live in allows me to do anything I want so I don't have to have any permits or planning permission etc but some towns and cities may differ and may require the permit etc.
I would check with the town or city you live in to see if you can add a fence to your front yard and how far back you have to put it from the sidewalk.
Still your property line is usually right up to the sidewalk anyway so you can usually put the privacy fence right up to the sidewalk.