Like Reignmaker stated, you don't need a round pen.
However, if you would like to have the "support" of one - you can make one on the ground in a variety of ways for visual aid for you (as it wouldn't actually "contain" your horse). The simpliest would be lime or some type of powder - drawing a circle (mine would be lopsided!! ROFLMAO) on the ground. The best way to get the circle is to "make" a compass. Put a stake in the ground where you want the center of your "round pen", attach a string 1/2 the width of your finished "r-pen" and walk it around. If you want a 30' circle, you'd use a string 15' long. Haystring works well for this! I also use this trick to put the posts in the ground for my "r-pen". You can use a corner of a fence in your paddock or yard as 1 or 2 sides (so that section is "straight" - who cares?).
IF drawing it doesn't work, then again use your "string compass", and use bricks, weighted containers (coffee cans, laundry containers, little water bottles, 2 ltr bottles, ??) and put them out like posts in your circle. Or use boards, landscaping timbers - etc - you get the idea. Who said a round pen had to be permanent when it's a training aid? Unless you want to do free lounging or use it as a pen, there are lots of ways to use visual aids for an "arena" - even a simple stake in the ground w/ a paper plate attached as a marker (think dressage arena).
if you want more substantial, you can put up step in posts and use some type of rope. Or put up actual posts with rope. Or use the 16' panels like I've used and you can build either a temporary or a permanent r-pen using them. The smallest circle I would use would be 30' and go up from there.
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If you aren't comfortable with "stretchie" side reins, you could also do balancing side reins. For those you use a solid "line" and put it in the shape of a "v". You can use two separate lines - one on each side (for lounging circles, you will need to re-adjust them when you switch directions or have them just loose enough that they can bend - but understand that they won't be able to do a deep, rounded body bend) OR you could do one continuous line (clothesline or paracord works really well for this) doing your "v" at the top by running it thru the ring at the top of your surcingle or around the terret that the check attaches to (allowing the cord to move freely so that they can bend/turn). Then you can adjust how much tension you want on his head/mouth and he can have freedom to move his head up and down while learning to carry the bit and give/get soft. If you use a continuous line, he can bend as deep as you like provided the cord moves freely. All string - even hay string - has some stretch, so no worries there unless you make it short enough to crank his chin into his chest (don't think you'd do that) - this set up is pretty forgiving while working wonders!
I did experiment with making some balancing side reins and have used just simple hay string tied from the girth thru the bit to the surcingle again... I only have pics of this - lets see if the hotel connection will let me add pictures now?