You can set a gray scale to measure salinity and this should be evaluated in the field and once the scale established for similar work areas.

Try the normalized Salinity index:

Landsat TM:

(band3 – band4) / (band3 + band4)

or Landsat 8/OLI:

(band4 – band5) / (band4 + band5)

If you don't have any vegetation cover and soil is dry at time of mapping you can use different band combinations, including the SWIR and the MIR in addition to one visible band.

Thank you so much for your responses

You can use Hyperion EO-1 image which can give you thousands of indices suitable for you analysis.

Dear Glory,

There is a very nice book about your question and more on remote sensing and soil salinity:

"Remote sensing of soil salinization, Impact on Land management, Eds. Graciela Metternicht and J.Alfred Zinck. CRC press. taylor and Francis group. Boca rotan 2009."

According to the this book even the hyperspectral sensors were not very sufficient on soil salinity detection by remote sensing however, some of the studies showed that significant relationship with soil surface salinity and SWIR wavebands ranged around 1450nm, 1950nm and 2450nm.  

Thank you Onur. I will check on the recommended book.