No - there is too little infra-red light remaining.

Energy from a star or Sun dissipates into a sphere of surface 4∏d^2 (d is distance from object). So energy from star will be r^2/R^2  of Sun's (r Sun distance, R star's). Assume star is of the same output as our Sun and you can see how very little energy the starlight contains when it arrives at the Earth.

In general I agree with PF, but it is not so much that there is too little infrared remaining, but too little energy in light of any wavelength. In fact, IR is in general rather better at passing through space than visible light is.  If you had a lens the size of the solar system, you might be able to concentrate the light of a nearby star enough to light something, but I'd hate to have to demonstrate it!

You could certainly in principle concentrate a star's light (even apart from Sol's) to achieve the right temperature at the focus, but the spot would be so small that the heat would conduct away faster than would permit it to ignite anything but certain extremely reactive chemicals, perhaps such as microscopic crystals of certain explosives.  There is a certain threshold to exceed before you can ignite most substances.

When I was a kid I had a magnifying glass that was about 3 inches in diameter and a good fire starter in summer. The area of the lens was then, lets say, 7 sq inches.

Our sun, by definition is 1 AU (astronomical unit) away. The next nearest star is 268000 AU away. Assuming that that star has the same output as our own, the power per square inch reaching earth is 1/268000^2 times that from the sun (inverse square law). The size of the lens that we would need to start a fire would be 7 x 268000^2 sq inches or a diameter of 800090 inches, or 66674 feet.

Sirius, the brightest star as seen from earth, seems the obvious candidate. It has 25x the luminosity of the sun, but is about 500000x further away. So your lens/ mirror needs have a 500000/25= 20000x larger diameter than you would normally need.

How large does a lens have to be at least to burn paper using the sun ? It depends what you mean with burning. If you search the web on paper burning using lasers, you will see mostly charring paper starting at about 500mW. As the sun radiates at about 1mW/mm2 you need a lens with a 500mm2 surface or 25 mm diameter. Using Sirius you would need a 0.5 km diameter lens or mirror for the same effect.

I certainly appreciate the contributions of SH and HU, who bothered to work it out instead of handwaving as I did!

Mind you, given the sizes of lens they very plausibly came up with, I still would not like to have to do it to prove it is possible! Not even with Fresnel lens or mirror arrays in space. ;-)