An optical true time delay line (OTTDL) is a basic photonic building block that enables many microwave photonic and optical processing operations. The conventional design for an integrated OTTDL that is based on spatial diversity uses a length-variable waveguide array to create the optical time delays, which can introduce complexities in the integrated circuit design. Here we report the first ever demonstration of an integrated index-variable OTTDL that exploits spatial diversity in an equal length waveguide array. The approach uses subwavelength grating waveguides in silicon-on-insulator (SOI), which enables the realization of OTTDLs having a simple geometry and that occupy a compact chip area. Moreover, compared to conventional wavelength-variable delay lines with a few THz operation bandwidth, our index-variable OTTDL has an extremely broad operation bandwidth practically exceeding several tens of THz, which supports operation for various input optical signals with broad ranges of central wavelength and bandwidth.