Is it possible to use the pushups as biceps workout by changing the position of hands? I searched the net for bicep pushups and tried it. I don't know about my biceps but my wrists were very sore. Is it because the bicep muscle is used to turn the wrists? However, I am not sure if I used the correct method. Can someone explain the correct method or provide some reliable link?
Bicep workout is a pulling workout. Pushing ones targets your shoulders, chest and triceps to large extent. They target biceps too, but not as much as pulling and curling do. Having said that, muscles growth happens all over your body, and not in a specific area. So, in order to tone or build bicep, you need to do full body workout. Even while doing regular pushups, biceps undergo contraction and relaxation, but if you just do pushups to gain biceps, I don't think you'd end up with the results you are trying to achieve. I'd suggest along with pushups and other body workouts, try doing resistance band exercises, if you have no time to hit the gym and want to do it at home. Those bands are really cheap and available online or at any gym store.
You have two fundamental issues here. First, a push-up is, as per its name, primarily a pushing exercise, while biceps are used for pulling, so it's only on the negative movement that you'd be targeting the biceps. Secondly, a pushup properly done targets the torso as much or more than the arms. Which leads us to a fundamental question, why push-ups? Is it because you want a bodyweight exercise? Because you're trying to avoid needing equipment?
If you don't actually have something to do bicep curls with, I'd recommend an inverted row instead. You can do it with a waist-high bar or the edge of a table, so there aren't many equipment requirements. To work the biceps and back, use an underhand grip. As with push-ups, it's the entire upper torso that's used. If you're looking to isolate the biceps, and want to avoid having to buy barbells, your best bet is to either improvise weights (plastic bags or bookbags with canned goods in them aren't a bad substitute. Filled milk jugs work too) or to provide bodyweight resistance via a towel that you're pushing down on with one foot (also works balance). There aren't really any non-equipment bicep exercises, but there are some good ones with little equipment.