Another way you could do this if you don't have access to either a wavemeter or stable reference laser is to scan the laser across an interferometer with a known free spectral range with several peaks in the tuning range. Finding the frequency deviation is then just a matter of counting the number of fringes that go by as you tune the laser, then multiplying by the free spectral range to get frequency change. This solution won't give you the center frequency of the laser, just the relative change. One nice aspect of this approach is that it can be done both slowly or at high rate with a current chirp. At high rate, you can use this approach measure the dynamic response of the laser (ie, see it tune faster/slower during a linear current ramp) and calibrate accordingly.
If you lack an interferometer with a short enough FSR, you can build a Fabry-Perot with two optical half-mirrored flats or wedges and a detector. That way you can make the FSR as short as you like, though you'll need ~1.5 m for a 100 MHz FSR, and alignment will be a fun exercise.
Worth repeating that effective temperature control of the laser is really helpful for this kind of measurement. Here are two more variations.
Absorption cell reference
I had decent results for 1542 nm DFB lasers, using a 13C2H2 acetylene absorption cell as reference. The laser had TE cooler and thermistor integrated into the package, which simplified temperature control. Tuning over the P14, P15 and P16 absorptions at fixed drive current gave the temperature tuning rate.
P16 1542.38372 nm 194369.569 GHz
P15 1541.77244 nm 194446.632 GHz
P14 1541.16699 nm 194523.021 GHz
After calculating the temperature coefficient, I tuned to one of the peaks, then applied a small temperature offset, and found the drive current to return to the peak.
Temperature coefficient was around 11.5 - 12 GHz/K
Current coefficient approximately 430 - 570 MHz / mA.
Expect different results for other devices.
FIbre interferometer
If your laser is fibre pigtailed, an alternative to Aaron's 1.5 m long free space cavity is to configure a fibre Mach-Zehnder interferometer using a pair of 3 dB 2x2 directional couplers with a suitable path length difference between the two arms.
Polarisation-maintaining fibre is helpful, but not essential. With standard fibre, a polarisation controller in the long arm may help if fringe visibility is poor, but you can probably manage with a couple of fibre loops taped to something stable whose orientation you can adjust, as the alignment need not be perfect. Keep the temperature stable, for example by placing the passive components of the interferometer in an insulated box.
Using standard single mode fibre, 1 m path length difference will give 204 MHz FSR at 1540 nm. Corning SMF 28e+ fibre has effective group index of refraction 1.4674 at 1310 nm and 1.4679 at 1550 nm.
Dear all , Thank you so much for your invaluable comments. I am going to try @Aaron Daniel Marsh method first as I have fabry perot interferometer and see the what I get.