Yes. Get two identical mics, condensors if you can afford them, if not then SM-57s. You also need at least a two channel audio interface with two or more mic preamps. Bare minimum total is about $300 - $400 (US) new. If you can afford more than two channels with more than two mic pres and a third mic, that's even better. A kick mic like a D112 will be fine for the third but an SM7, RE-20, or MD-421 would be best if you can swing one of those for mic three.
Do a web search for "recorderman mic technique" or "recorderman overheads" to find the complete guide to this mic setup. It's a modified Glyn Johns technique that gives a great stereo spread and full sound with solid time alignment with just two mics. Basically you position one mic over the hi hats, another behind the right shoulder of the drummer, and you use a piece of string, rope, or even a cable to measure and match the distances from the mics to the kick and share.
If you have three mics then put the third on kick, but not right in the hole. Give it one to five feet and just move it around until it sounds best.
If you can afford more mics and channels, then either one or two room mics if you have a good room and want that sound, or start doing spot mics on snare and toms. You can use SM57s or 58s for these, or MD-421s if you can. I like a large diaghram condensor on snare but that's moving into higher budget territory.
Overall, start with fewer mics of higher quality that you can keep and use forever (my oldest mic is the first one I got: SM-57 from 20+ years ago and I still use it) and you can expand your mic locker through the years until you have a pro collection.
Start by researching the recorderman technique.
Edit: here's a link to a good guide to recorderman miking: http://jonstinson.com/the-recorder-man-drum-miking-technique/
- first mic over the snare (maybe a little over the hat) pointed right at the snare two drumsticks away from center of the snare
- second mic behind the drummer over the opposite shoulder pointed at the snare center also two drum sticks away
- use the kick pedal to clamp a cable or string to the kick head, run the cable/string up to one mic, then down to the center of the snare head and hold it there. Take the point on the cable touching the mic and move it over to the other mic and make sure the distances are the same. Adjust the mics slightly until they match. Normally two people are needed for this part.
The reason I continue to use this technique for overheads, even with lots of spot mics on the kit pieces, is that it gets the kit very well without relying on a good room. The most expensive part of awesome drum sounds is building or renting a great sounding, large room. With recorderman I've gotten great sound in a small, tin-lined storage space. Actually a great drummer is the most expensive part, then a great room. I'll take a great drummer and two SM-57s in a plastic shack over a flat sounding drummer who can't tune drums and a dream mic locker at my choice of studio every time.