TARA (Telescope Array Radar) is a cosmic ray radar detection experiment colocated with Telescope Array, the conventional surface scintillation detector (SD) and fluorescence telescope detector (FD) near Delta, Utah, U.S.A. The TARA detector combines a 40 kW, 54.1 MHz VHF transmitter and high-gain transmitting antenna which broadcasts the radar carrier over the SD array and within the FD field of view, towards a 250 MS/s DAQ receiver. TARA has been collecting data since 2013 with the primary goal of observing the radar signatures of extensive air showers (EAS). Simulations indicate that echoes are expected to be short in duration (∼ 10 μs) and exhibit rapidly changing frequency, with rates on the order 1 MHz/μs. The EAS radar cross-section (RCS) is currently unknown although it is the subject of over 70 years of speculation. A novel signal search technique is described in which the expected radar echo of a particular air shower is used as a matched filter template and compared to waveforms obtained by triggering the radar DAQ using the Telescope Array fluorescence detector. No evidence for the scattering of radio frequency radiation by EAS is obtained to date. We report the first quantitative RCS upper limits using EAS that triggered the Telescope Array Fluorescence Detector. <P />The transmitter is under the direct control of experimenters, and in a radio-quiet area isolated from other radio frequency (RF) sources. The power and radiation pattern are known at all times.&lt;/ce:para&gt; <P />Forward power up to 40 kW and gain exceeding 20 dB maximize energy density in the radar field.&lt;/ce:para&gt; <P />Continuous wave (CW) transmission gives 100% duty cycle, as opposed to pulsed radar.&lt;/ce:para&gt; <P />TARA utilizes a high sample rate DAQ (250 MS/s).&lt;/ce:para&gt; <P />TARA is colocated with a large state-of-the-art conventional CR observatory, allowing the radar data stream to be sampled at the arrival times of known cosmic ray events.&lt;/ce:para&gt; <P />&lt;/ce:para&gt;Each of these attributes of the TARA detector has been discussed in detail in the literature [8]. A map showing the TA SD array and the location of the TARA transmitter and receiver is shown in Fig. 1.&lt;/ce:para&gt;Section 2 of this paper includes a description of air shower plasmas and possible radio scattering mechanisms. Theoretical and experimental parameters that influence radio scattering are presented and discussed. We justify use of the thin wire model in a radar echo simulation that predicts echo waveforms, which we will subsequently (Section 6) use in placing limits on the air shower radar cross section (RCS). Sections 3 and 4 describe TARA data and offline processing techniques. In Section 5, we describe the signal search using simulated waveforms as matched filter (MF) templates in order to maximize sensitivity. Section 6 describes the procedure for calculating a scale factor to the RCS model described in Section 2, the results of which are used in placing the first quantitative upper limit on the EAS radar cross-section (RCS). In Section 7 we summarize these results and discuss the viability of radar detection of cosmic rays in light of the TARA findings.&lt;/ce:para&gt;&lt;/ce:section&gt; <P />...