Acrylic paint is sold in different viscosities for different purposes. It is basically acrylic medium plus pigment. The acrylic medium is the binder that holds the pigment together when it dries. It's watery, and depends on the water to keep the acrylic polymer dilute so it doesn't start to cure. If you let it start to dry, it will begin to cure. That will give you a short working period when the paint is more viscous, but it isn't really a solution to your problem.
The pigment can consist of colored and non-colored powders that don't go into solution. Non-colored pigments can be used as thickeners or to add inexpensive bulk. The colored pigment is the expensive part, and also acts like a thickener. What you need is more pigment, best added in the form of a paste-consistency material that adds more binder.
If you have a very similar color in thicker acrylic paint, you can mix in some of that to thicken it. Otherwise, there are some things you can add to your paint to thicken it. Some will affect the color and some will affect the opacity without changing the color much. Some can affect the glossiness of the dried paint.
Your best bet is heavy-body acrylic gel medium designed as a thickener. This is a paste-like acrylic gel that looks white/translucent, but dries clear. It will thicken the paint, but will also further dilute the already-sparing pigment. Depending on how much you add, it could affect the opacity, so it could potentially require several coats or a thicker coat. Since the gel medium contains its own binder, it won't degrade the strength of the dried paint film.
There are other materials you can use to thicken the paint, but they typically add white, which will desaturate the color, and may affect the strength of the paint film. These include:
- modelling paste
- paste made from talcum powder and either PVA glue or Mod Podge
People have used a paste made from cooking starch or flour with water, but the resulting paint is likely to get attacked by micro-organisms. You can thicken the paint with various dry powders, but that is likely to make the paint film brittle.
Joachim raises a good point in a comment that if the miniatures are plastic, any additive could affect how well the paint adheres if your paint is specifically formulated for plastic. It may take some experimentation, and any effect will be tied to the amount of material you add. You can always prime the miniatures.