We guitarists often tend to use, or even overuse arpeggios in solos. It's hard to name several of your guitar heroes who don't do it, also. Actually, they're the ones who popularized it, which is awesome! Arpeggio technique on electric guitar is one of my favorites, and for that exact reason I began searching for possibilities of including them in rhythm parts.
It's good to get around in all sorts of genres, and in your favorite you have to be the best as you can. Using arpeggios in playing rhythm parts might help you stand out a bit, and explore additional ways to spice up your music. I definitely advise that you first take some of your favorite rhythm parts and rearrange them so they have arpeggio fills, without loosing the vibe or feel of the music. Then, explore some totally different music genres and learn how to do it there. That will reflect on perception of your music domain in extremely positive way.
How I use arpeggio phrases in rhythm parts
The easiest way for me to do it is to take a simple rhythm part and then slowly add arpeggiated ornaments within it. The best way to demonstrate this is through examples. Here's a very common funky riff. You have probably played something like this numerous times.
Note that you have to play this sort of riffs gently, and be tight in time. It won't sound good otherwise. Also, if you're after that "chaka-chaka" sound you can hear at many funky guitarists, that's a result of gentle strumming somewhere between pick and thumb, and also pickup and guitar wood combination. Mahogany woods with single-coil picks do the trick for me, yet, it's possible to get it through other variations and setup.
Now, let's add arpeggio phrases within this riff. It's really important that the feel of the riff doesn't change. It actually must fit the composition just as this one would. That's the point here, to include arpeggios, but do it with taste. This is just one of many possibilities - to put it at the end of each strumming bar.
What I've done is played the whole chord of the key I'm in through arpeggio phrase. This is really simple, but it opens lots of options if you haven't given it a thought before.
Alrighty, our next example will be in a more "rockish" manner. In a key of A Dorian and pretty known approach, you might find this interesting to experiment with.
What I decided to do here is emphasise those G and D chords at the end of the riff, in the last bar. Both are major chords, so it will do me good to go for their major thirds and then arpeggiate to fifth and the octave.
Let me tell you that when you're recording in a studio as a session musician, for example, unless you're doing straight note reading, producers will love small ornaments like that. They will make their recordings sound different, which is always good. If you'll play a lot with such approaches, you'll encounter plenty of ideas unique to you, which will get really worthy.
Another approach you might really like is that you take a riff and then completely replace it with arpeggiated phrases. Sometimes that will work in the song, and another times it won't, but it's worth playing around with it. We'll go for it with a simple strumming theme;
Take a look at each chord in the progression and take out all the notes that really make that progression be memorable and melodic. Start with those and arpeggiate them until you get more notes in the same key that work together as a phrase. I came up with this simple arpeggiated riff, where nothing except melodic statement has changed. The feel and vibe of the riff remained the same, which, as I emphasized several times before, is very important. You don't want to change song, you just want to spice it up a bit. Here's my riff;
Through these 3 examples I have given you basic directions on what you can do to start implementing arpeggios in your rhythm playing.
You can download Guitar Pro files along with the whole article here. If you have problems with understanding arpeggio phrases and creating your own phrases you should definitely check my e-book "(Overcome) The Arpeggio World". There are hundreds of examples you can learn from and lots of other explanations you might find helpful.
Now, get back to your guitar and do me a favor. Don't put it away until you make 10 arpeggiated versions of rhythm parts that you enjoy playing the most. This is all about creativity, and it takes lots of practice and even trial and error until you get to something cool. The key is to be persistend and enjoy the whole thing!